The 7D is a workhorse camera designed with professional shooters in mind. It's sort of a "1D Mark IV Lite", at one third the price. It does not have much support for inexperienced shooters. It's capable in most any environment, but in effect you pay extra for it's high frame rate and AI Servo/Action/Sports oriented focusing system, that's a lot more complex and needs to be set up correctly. It's a very capable camera, well made, solid, a bit on the heavy side even, pretty reliable and durable, and reasonably well sealed against all the nasty things that come with shooting in difficult situations.
Learn to use a 7D well, and it can do you proud. It takes some commitment to get good with one. If you are a serious amateur willing to work at learning the camera and setting it up properly, then it might be a really good choice.
However, if you want a camera for family photos and rather more sedate general purpose use, you have other excellent possibilities too, most at much less cost. One thing you don't have to worry about is image quality. All the current APS-C format Canon (T2i, T3i, T4i, 60D and 7D) use essentially the same 18MP sensor and are capable of delivering virtually the same image quality. The lenses used on them will make far, far more difference than the camera behind them, as you noted. And, that $2000-2500 budget will evaporate before you know it. Besides, I don't know where you are seeing 7D for $1000-1200... looks to me as if B&H is asking $1450 for them right now. And $900 for 60D (after a $100 instant rebate).
60D is currently probably a better choice for what you want to shoot and your level of experience. It has a simpler, but still quite capable AF system and a bit slower, but still fairly impressive frame rate (about 5 fps instead of 8 fps that the 7D can do). It is a pentaprism model, which will give you slightly bigger and brighter viewing than you see with your Rebel models and their penta-mirror arrangement.
So, I'd suggest 60D..... but right now I think you should wait a couple months to see if a 70D is announced. Often Canon rolls out new models at or just before the Photokina trade show, which is Sept. 18-23 this year. Sometimes they announce a new consumer model a bit later, for the Christmas buying season. A hint might be that there is currently a rebate on 60D. (And not on 7D... I seriously doubt there will be a 7D "Mark II" announced, also because Canon just rolled out the unusually comprehensive firmware revision for the current model this month.... why would they do that if they have a new model right around the corner?)
But, I would suggest instead that you concentrate on lenses now, get some experience with them on your current camera, and wait a bit before buying a camera. Let's see if a new 70D is announced in the next month or two.
So, I'd like to comment a bit about the lenses you're considering...
- EF-S 17-55/2.8 IS is a very good solid choice as a mid-range "walkaround" zoom. Get it and the hood to fit it. It's sharp, fast/accurate focusing, a top performer in all respects. It is not an L (no EF-S lens ever will be, by definition), so isn't sealed as well and there's more plastic in its construction... but the image quality from it rivals any L-series lens, and that's what really counts.
- EF 40/2.8 STM "Pancake".... Forget it. The 17-55 provides you with a 40mm focal length with f2.8 max aperture. Plus, AFAIK, only the T4i can take full advantage of the STM "stepper motor" of the lens, a feature that's particularly important for video, not stills. So there's little or nothing to be gained getting this lens, unless you just want something small and pocketable (but are putting it on a larger camera, so that's sort of self-defeating).
- EF 50/1.8 or 50/1.4 or Sigma 50/1.4.... I'd recommend one of these instead of the "pancake". Sure, they also duplicate a focal length of the 17-55, but they are up to two stops faster than that zoom. These act as "short telephoto/portrait" lenses on an APS-C format camera. Great for low light, and for those family/baby portraits. The Canon 50/1.8 is inexpensive and very entry level quality build, but capable of nice images. I'd recommend it for someone wanting to use it for an occasional portrait. Both the Canon and Sigma f1.4 lenses give a bit nicer image qualities and faster/more accurate focus, and have 2/3 stop larger aperture available. They also are better built and more durable, but of course cost about 3X or 4X as much! The Sigma is fairly large and heavy, compared to either of the Canon.
- EF-S 10-22 USM.... is a fine choice for an ultrawide. Very capable. It's one of the best, but also one of the most expensive UWA zooms. You mention about 20% usage for the types of photography where you are most likely to use this sort of lens... so you might want to consider some close alternatives, that are less expensive. I'd suggest at least looking at: Sigma 10-22/3.5 HSM and the same but less expensive with a variable aperture; Tokina 11-16/2.8 and 12-24/4; Tamron 10-24. All of these are less expensive, but pretty capable. Personally I use the Tokina 12-24 and am happy with it. There is now also a super wide angle Sigma 8-16mm, the widest lens available aside from a fisheye, but it's priced close to the Canon 10-22. If you get the Canon, buy the lens hood too, which is sold separately. All the others here come with a hood.
- EF-S 55-250 IS.... This is an okay, entry level lens. For a couple hundred bucks it has surprisingly good image quality and it's fairly compact and lightweight. However, it's AF is slow and less accurate than a lens with USM. And, it's not built "for the long run" and there are other good options. Mainly, I'd suggest considering the 70-200/4L IS.... it's a killer lens, built like a tank, with fast and accurate USM focus. Yes, it's a lot more expensive... But if you save money elsewhere and can work it into your budget, this would be a great option. If the cost is too much of a stretch, the non-IS version of the lens might be an alternative. But IS is really nice to have on these longer focal lengths! There are few pro Canon shooters who don't have one or the other of the 70-200s in their kit. That might be a clue. The f2.8 versions are great lenses too... but more expensive, bigger and heavier.
As to the flash, pick up a 430EX or even a used 420EX, 550EX, 580EX. The built in flash is a joke and near worthless on any of these cameras. It is a heavy draw on the battery charge and still is weak and anemic... plus it's located in the worst possible place for redeye and ugly shadow effects. I'd suggest one of the accessory flashes... even the highly automated 220/230/270EX would be a big improvement over the built-in flash. I do suggest a flash bracket and an off-camera shoe cord, to put the flash off to the side and a bit further above the lens, which makes for even nicer lighting. These items are available generically off eBay or elsewhere, for not a lot of money.
Memory cards... well it depends on the camera model you get what type you'll need (60D uses SD, 7D uses Compact Flash)... Personally I use mostly 8GB cards... fourteen of them in a pair of 7Ds. I get close to 300 RAW files per card, in normal use. I have a couple 16GB cards, but mostly use them in my 5D Mark II, with it's somewhat larger files. I just am a strong believer in not putting all my eggs in one basket! There are often sales on memory cards... I recently noticed a two-pack of Lexar 400X UDMA 16GB CF cards were right at $100. I don't watch the price of SD memory, since none of my cameras use it.
Whatever camera you get, you are very likely going to want a spare battery or two. The 7D and 60D both use LP-E6, with give almost twice as many shots per charge as the LP-E8 the Rebel series cameras use now. It depends a lot on whether or not you use the built-in flash and how much you playback images and use the rear LCD to navigate the menus, since those things gobble up power a lot more than anything else on a camera. Using a pair of LP-E6 in the grip on one of my 7Ds, I can shoot well over 2000 images without changing batteries.... probably closer to 3000. So I bet I get 1200-1500 images per battery charge. But I never use the built in flash and only occasionally spot check images/histograms on the rear LCD. With earlier BP511/512 series batteries (such as those used in your 300D), I always carried two extras for every one in my cameras. Now with the LP-E6 in both my 7Ds and 5DII, I carry one extra. If I were using the Rebel series cameras with their LP-E8s, I'd have to carry two extras per. These newer batteries are more expensive, but I find I don't need as many spares. So it probably works out close to the same.
No, I wouldn't tell you to go straight to a full frame camera. In fact, the crop sensor cameras have quite a few advantages for a lot of people. They can be used with a wider choice of lenses (since all "crop only/EF-D" and all "full frame/EF" lenses will fit and work on them). And, lenses can be smaller, lighter and less expensive. Full frame has some advantages, too.... And I use one myself... but I think it's vastly overhyped here and most people would be better served sticking with crop cameras.