In TF2 the gametype comes from the map you load. The map prefix decides the rules: pick a gametype on the deploy form and it filters the maps to match, or change map any time from the web console. Every map in the picker has a bot navigation mesh, so bots work on all of them.
King of the Hill (koth_)
One central control point. Hold it until your timer runs out. Fast, easy to read, great for small groups and great for bots. Maps: Viaduct, Harvest, Lakeside, Sawmill, Suijin, Highpass, Nucleus, Badlands.
Payload (pl_)
Blue pushes a cart along a track, Red defends. The signature TF2 mode. Bots push and defend competently. Maps: Badwater Basin, Upward, Goldrush, Thunder Mountain, Frontier, Barnblitz.
Attack/Defend (cp_)
Blue captures points in order, Red holds the line. A control point variant. Maps: Dustbowl, Gorge, Gravel Pit, Steel, Junction, Mountain Lab, Egypt.
Control Point (cp_)
Five points, both teams can capture. Push to the enemy last point to win. The classic competitive format. Maps: Process, Gullywash, Snakewater, Badlands, Granary, Well.
Capture the Flag (ctf_)
Steal the enemy intelligence and bring it home. Maps: 2Fort, Turbine, Double Cross, Sawmill, Well. Honest heads up: bots do not play CTF well (they rarely grab or cap the intel), so CTF is best with a room full of humans. Add a few bots to fill out the fight, but do not expect them to win the objective.
Arena (arena_)
One life per round, no respawns, last team standing wins. Tense and quick. Maps: Lumberyard, Watchtower, Badlands, Nucleus, Granary, Sawmill.
Picking on deploy
Choose a gametype, then a starting map from that gametype. Default is King of the Hill on Viaduct, which is the friendliest start for a small group with bots. Change map or gametype any time from the web console (it briefly reloads).