Pretty much anything off-the-shelf will do, yeah. Tubulars are the exception, not the rule, so to speak.
The only issue you may need to look at is width of the tyre; some frames/brakes are thin and don't give much room for wider tyres. For example, my road bike will only accept up to 28mm width tyres, and even then, with the brake caliper in its 'release' position the sides of the tyre still rub the pads a bit when slotting the wheel in.