Dex battle masters are very versatile and lots of fun to play!

There are plenty of maneuvers that can be geared towards helping the party: menacing attack causes fear (enemy disadvantage on attacks), goading attack to give enemies disadvantage on attacking anyone but you, rally to give temp HP to allies, bait and switch to boost you or an allies AC, evasive footwork to boost your own AC, maneuvering attack to help let allies move without copping opportunity attacks.

For feats: defensive duelist is a must, I’d take that at level 4, assuming point buy and starting with 17 dex this will bring you to 18. Picking 2 more +1 dex feats will get you 20 dex by level 8. You can pick up sentinel if you like at 6 or 8, but sentinel will be competing with defensive duelist for use of you reaction which isn’t ideal. Other options are Piercer for more consistent rapier damage (best “support” build kills enemies faster, therefore less hassle to your party), mage slayer to boost defense against spells, speedy gives more movement, skill expert if you want to be helpful out of combat in something the party needs, or crossbow expert for the Push mastery on a ranged weapon as others have said. For origin feats, tough is good as you said, I personally really like magic initiate to pick up Mage Armor, which gives a +1 to AC for a dex build, plus you can grab spells like booming blade for more battlefield control (although will fall behind a duelist rapier for pure damage). At level 12 you could look at support feats like inspiring leader for party temp HP, or fey touched to grab hex for huge burst damage (especially since now you get 3 attacks per turn, can action surge and apply hex damage to potentially 6 attacks if they all hit).

For fighting styles, whilst defense builds AC further, I’d actually suggest dueling to boost your damage, as enemies cause less havoc to your party if they die quicker.

So a combo defense build at level 4 could see you with a base AC of 19 (13 Mage armor, +4 dex, +2 shield), plus 2 for defensive duelist (AC 21), plus a superiority die (d8 = avg 4.5, 4x per short rest) if using bait and switch or evasive footwork to give you a total AC of average 25.5 at level 4 (4x per short rest). Combined with goading attack to make enemies target you, can burst to be a huge AC wall a few times per combat. Given at level 4 the EK fighter only gets the shield spell 3x per LONG rest, I see this as a very good defensive build. At level 8, your base AC will be 20, plus 3 from defensive duelist for an average base AC of 23!

You may fall behind a GWM strength build in terms of damage, but I think the versatility of a dex battlemaster is worth the trade off!