I have a 2014 Trek 1.2 and have logged close to 10K miles on this bike and I like it, but the rear cassette is starting to show some wear, I want better breaking, and an accident several months ago has my rear shifter rather banged up. Based on the cost of individual components, I'm wondering if I should just replace the entire groupset with the Sora R3000, or replace just the cassette and shifters, then go with a better brakes. What I'm not sure of is whether a Tiagra or 105 will fit the frame.

Of course, if the chain/cassette are worn out they should be replaced. If you haven't replaced the chain in 10K miles the chainrings are probably shot too.

There shouldn't be anything wrong with your brakes. But you might want better brake pads. Kool Stop salmon are the best. It's also likely that your brakes aren't setup as well as they could be. The fanciest brakes in the world won't fix poor setup.

You can upgrade whatever you want, Tiagra or 105 will fit that bike. But to me, it would make the most sense to just replace the cassette/chain and busted shifter.

You should definitely replace the cassette and chain.

The no-name dual pivot calipers on your Trek 1.2 would probably work much better with decent pads like FastJake recommended, but those brakes did get called out on at least one review for being sub-par. I couldn't fault you for replacing them if that's what you chose to do.

My overall recommendation is just a little bit different than Jake's: I'd replace the cassette & chain, shifter, and brakes -- choosing brake calipers to match your levers' pull ratio.

So then it's a matter of comparing costs for those parts versus the cost of a replacement groupset. It looks like buying just the necessary parts could save you about $100. On the other hand, going for a complete groupset will replace all wear items (shifters, chainrings, bottom bracket) and gives you an opportunity to upgrade to 10-speed or change your gearing if you'd like.

(All prices from Ribble unless noted otherwise)

INDIVIDUAL PARTS:
Shimano Sora 3500 right shifter $69.99 (Jenson)
Shimano Sora 3500 Brakes: $26.42
KMC x9.73 Chain: $10.56
Shimano HG400 9-speed 11-28 Cassette: $18.91
TOTAL: $125.88

COMPLETE GROUPSETS:
(levers, derailleurs, brakes, crankset, bottom bracket, cassette, & chain)
Shimano Sora R3000 9-speed Groupset: $222.58
Shimano Tiagra 4700 10-speed Groupset: $323.48 (Wiggle)
Campagnolo Veloce 10-speed Groupset: $333.87 (Wiggle)

My recommendation would probably be to get new cassette, chain, and brakes. How banged up is your right shifter? You can get replacement hoods if that's what's mostly scuffed up and if they work OK.

For the brakes, I'd buy Shimano brakes--Sora would be fine. Technically, current Tiagra/105/Ultegra/DA use slightly different cable pull than your Sora levers, so you'd probably get the best performance using current Sora or older high end components. You could try new brake pads, but the stock brakes really aren't that great. A compromise would be to put new pads on the rear brake, and put a Shimano on the front (this is how my Supersix is set up). If your chainrings are worn it's probably worth it to replace the crankset wholesale with Sora--it'll probably shift better than the original chainrings, and likely drop a fair bit of weight with a 24mm spindle and external bb.

If you do want to upgrade the drivetrain, you can keep your derailleurs if you want if you use 9 speed Sora, or 10 speed 105 or Ultegra. Tiagra 10 speed is INCOMPATIBLE with other 10 speed components (unofficially, the derailleurs are actually 11 speed compatible). If you want to put an 11 speed drivetrain on the bike, you will need a new rear wheel with an 11 speed freehub body. If you were doing a complete drivetrain upgrade, I'd probably recommend the current generation Tiagra, as it has a longer cable pull ratio than previous 10 speed groups that shifts really well with great reliability.

If you are replacing the rear shifter, cassette & chain, now would be a good time to upgrade to 10 speed if you want.