It can very difficult to find wood that requires minimal milling, but it is possible. The tradeoff is that you may need to spend a lot of time searching through every board to find the one or two that are straighter than others.
Look for wide, 4/4 (1") or thicker boards with few knots. These come from larger trees and are generally more stable.
Look at the end grain, ideally searching for quartersawn material where the wood grain is perpendicular to the face (wide side) of the board.
Generally, the lumber used in construction is not suitable for fine woodworking without additional milling. Some home improvement stores also sell pre-glued panels and hardwood lumber (sometimes wrapped in plastic), but it usually costs significantly more than buying dimensional or rough-sawn lumber from a hardwood dealer.
If you do not have the tools to mill lumber on your own, call some local cabinet shops. Often they will sell you lumber and may even do some milling at little or no additional cost. You can also buy your lumber directly from a local sawmill or hardwood dealer, and they will typically surface the lumber on 2 or more sides for a small additional charge.
If you're tight on space, hand milling your lumber is always an option. If you prefer power tools, you may also want to consider looking into a combination jointer/thickness planer. Also, depending on what you're building, you may be able to build jigs to do most of your milling. A taper/straight-line rip jig will do the edge jointing, and you can build a separate jig to joint the faces of boards to about 6" wide (assuming you have a 10" table saw and can raise the blade to a little over 3").
Also look into community shops and rental stores. If you live near a community college or university, they may have a wood shop with all the tools you need to mill your lumber. My local university offers daily or monthly options, and larger cities have MakerSpaces where you can buy a membership and use the equipment. There is also a Habitat for Humanity "ReStore" in a town near me which rents out all kinds of woodworking equipment (including table saws and planers), though you must first purchase an annual membership.