For learning and being unobtrusive, a smaller and lighter camera and tripod is nice. Wide angle is necessary. I don't want to get too deep into hardware, but it appears to me that there is an interesting category of cameras that are mirror-less with larger sensors and large view screens. If I were you I would use the nicest point and shoot you own to experiment with and keep an eye on what that segment of the market is doing. In the old days photographers would put a towel over their heads and look at the image on the ground glass of a "view camera." Other than thinking about looking through the view finder, I would think about looking at the view screen. If you have a DSLR look for some type of view mode. Get a screen that will give you straight grid lines in your view screen. I can image the day when we will point a mirrorless camera like the GoPro and then look at a bluetooth app on our tables and do perspective and distortion correction and editing right there. Maybe even a distance away, not in the sun, under a towel. And the tablet will take one corrected and one raw image at the same time.
Ok. Don't buy a tilt and shift lens yet. But put the Canon 24 mm TS-E on your list to look at and shop for and wonder what body you would use with it. But for now, experiment with getting far enough back from your scene to point your camera directly level at the horizon and then get the building in the upper half of the view finder. You can crop later. A lot of the perspective problems come from pointing the camera up. The TS-E allows you to put the plane of the sensor parallel to the plane of what you are taking a picture of. You can do that without a tilt and shift lens, and just put your scene in the top half of your image. Go somewhere there are multiple columns with lots of vertical straight lines and with a hand held camera and look at the view screen and experiment with what you need to do to get the image on a handheld view screen to get all the vertical lines to look straight up and down. It will change your life. Shop for perspective correction software. If you point your camera at the horizon, then the perspective software has to do less to correct the perspective lines.
For learning and for lightweight compact camera setup, look at the Giottos MH1304-11C mini ball head that is on Amazon. And the Sima quick connect for tripod. These are excellent for smaller compact cameras. The head of any tripod you now have will unscrew off and you can put the ball head on, and then put the Sima quick connect on top of that, and your camera on top of that. Keep your camera on your tripod. Keep the legs of your tripod extended. Close the legs of the tripod, and swing the tripod up on your shoulder and walk around like that. Put a towel on your shoulder if your setup is heavy. Then to set up all you do is spread the legs of the tripod and you are good to go.
Look here for more information on other types and heavier duty options:
http://www.giottosusa.com/ballheads.shtml
If you use a heavier camera, you may want to look at a larger ball and the Giottos 652 quick release. But, as you can see, those larger Giottos quick releases would stick out from under a compact camera, more than the Sima quick connect.
Back in the film day when I had a Canon 24 mm TS-E, I had a Bogen 3039 that I see is now replaced by the Manfrotto 229. Wonderful setup. Look into something like that. Having this control of each axis suits some people's personalities more than others.
I enjoy testing the limits of smaller and lighter setups. Often people look at smaller, lighter, cheaper setups as more "beginner" setups that at some point you would grow out of into "real" photography. But I had bigger, heavier, more costly stuff back in the film days and now I enjoy lighter and smaller. Because it is all I need. Not because I am a beginner.
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