There is a lot to unpick, least of all is this was not a cheap bike when new. The specs I have found on the net shows components like SRAM Red 11 and an FSA SLK 386 50/34 crank. Replacing this with "inexpensive" as you have suggested is not thing you want to do lightly, even if it is an older bike.
If it is just worn teeth, easy and (should be) cheapest option is replacing the chain rings. I would recommend replacing both chainrings, along with the cassette and chain so you are starting with everything new. If you mix worn and new components the new components wear faster (and you never get the feel of a crisp, new drive line). The FSA SLK 386 50/34 crankset used a 110mm 4 bolt chainrings, but they are FSA's 'special' (as I understand) Asymmetrical Bolt Spacing, so do check any chainrings you order will fit. It is likely the only compatible chainrings are premium range product, so you may find a new (or used) crankset, with more standard chainrings provides a cheaper option.
The Bottom bracket on that bike is specified as a (press fit) BB386 (Evo), you will need a BB386 crankset if you replace the entire crankset. If you go this path, any BB386 compatible crankset should work.
Given you have also indicated your shifters are also on the way out, it would be prudent to cost replacing the entire group set, as group sets are often a lot cheaper way to buy components compared to individual items.