Laptop ???, for shooting tethered

I'm a huge fan of using Canon Utility Software for tethered shooting using my desktop...
I currently do a ton of photostacking and think that resolution is somewhat important...how important is it?
What kind of resolution/screen quality should concern me without getting stupid expensive?
This would be for use in the field.

Before picking a tool to do a job, you really need to define what that job is.

What do you actually want to do with the laptop? Do you want to do lots of processing and editing while you're on the move away from your main work station? Or do you want a tool for collecting and organizing data while you're on the go, while planning to do the actual processing once you get back home?

If all you want is something that lets you tether and do a general review of the image in the field, then you can probably get away with a fairly poor display and still be over and above what the camera's display offers you. If you want to stack images and do complete processing, then you'll want a higher end system to handle the more demanding task.

What Luckless said. I do a lot of remote shooting for photo-stitching (using Photoshop, ICE and Kolor Autopano Giga, depending on which one works best for a given subject) and we do the remote shooting using Android tablets of 7-8" diagonal (DSLR Controller or qDslrDashboard software on the tablets). When we stitch, the horsepower's more important than the screen resolution, since you can always zoom in to 100% on a "problem" area. So I'd say that first concern would be RAM (16 GB, or more if possible) and second would be processor speed.

It would be used for nothing more intense than the tethered stuff and normal teenage stuff...no PP at all, that is reserved for desktop system.

Then the resolution doesn't matter all that much. With either of the programs I mentioned, you could use an Android tablet with OTG cable (and have more control than EOS Utility offers). Add a $40 (or less) TP-Link MR-3040 with firmware from one of those two developers and you can even connect to any Canon with Live View, wirelessly.

If all the system needs to really do is connect to the camera and pull down images, then pretty much every modern laptop should be able to do that without breaking a sweat. Simple an inexpensive Intel Core i3 systems can be had for cheap, but do read reviews.

Your key factors are going to mostly be the general size/weight, and battery life. After that you would need to consider data volumes and flow. How much do you need to store at a given time? Would you be recording a small enough volume to easily work with an internal SSD in the 120-250GB range? (For cheaper systems) Or would you need to rely on hard disk drive storage, external, or paying extra for a larger internal SSD?

Something like a MacBook Air may meet your needs and have a very reliable build, or a similar style windows system, but do keep in mind that the aluminum bodies can have issues for field work, namely they get bloody cold in a hurry, and can be more prone to collecting dew than a plastic body.

*Edit:*
Personally I tend to suggest laptops, with a standard version of a mainstream operating system, over Tablets because I find the software is generally more robust and less prone to frustrating errors and annoying quirks. Things like native USB ports, and having multiples, can make work flows easier, and means less bits and pieces to keep track of over carrying an adaptor. However, most tablet solutions will probably cost a little less and be a little lighter, but possibly at the cost of transfer speeds and data storage options.

Lots of give and take in planning out something like this.

Try sitting down and writing out a story about how you would expect a shoot to go. Focus on details of your actions, and you can get a better idea of the solution that can work best for you.

The software that is used is solely windows based...