I second Altaco's suggestion of starting from a center and building outwards. Not only does it help with keeping everything flowing together smoothly, but it also makes it much easier to give the map rotational symmetry if you keep copying one side onto the other, rotating it 180 degrees. Far easier and less of a load on your computer than copy-pasting half a map.
For inspiration, look at existing maps you really like, then try to imitate the general design ideas used there (i.e. open areas connected via narrow hallways, multiple floors, etc - these are just examples, there are infinite ways to interpret TF2 mapping philosophies by looking at official and even community maps) but also consider problems found in the map/s you're using as inspiration (don't stick to just one - mix it up some!), then try to solve those in your design. Don't plagiarize though!
As for gamemodes, CTF and KOTH generally call for smaller maps than other gamemodes, so I agree with Altaco there as well - those are good to start with. CTF might be a little harder though since there's a lot more involved in getting flags from one end of the map to the other than in simply attempting to control the center of the map (i.e. you need more alternate routes, possibly a few tighter spaces, etc). From my experience with CTF (Well being a notable exception), CTF maps generally keep their intel in areas accessible via a series of narrow pathways off of the main or a secondary area. 2fort, Sawmill, and Turbine all are like this. Sawmill was also expanded from an Arena map (see below), making it a perfect example of the slightly larger nature of CTF.
Arena is basically KOTH minus respawning/resupply, no countdown timer, and a bit longer before the point becomes available (heck, Valve even converted Nucleus from Arena to KOTH
just by adding resupply lockers
), so it might also be a good place to start. Keep in mind however that KOTH tends to be favored over Arena gameplay-wise, so KOTH might be the way to go between those two.