What sound formats do I need?

Something to think about.
Are you able to move your viewing position rearward far enough to be under your existing ceiling speakers? If so, make those Atmos height speakers and simply add two more rears at ear level slightly behind or even with listening spot. Boom. 5.1.2 Atmos.
That’s what I did. Previously like you had 5.1 with ceiling rear surrounds.
Moved couch back 2 ft. Added wall mount (ear level) new rears.
Atmos is worth it IMO

with Atmos it is important that rear surrounds be near ear level. Do not put new rear surrounds in or near ceiling. They need to have vertical contrast with the height speakers. I initially made the mistake and mounted my new rears on wall behind near ceiling (since that was recommended with old Dolby surround). Nope, not any longer with Atmos. Had to switch their location

if you can move viewing position slightly rearward of existing ceiling speakers that is best outcome 

Dolby Atmos and DTS:X are new formats that allow for deciding on height / ceiling speakers.  They also don't necessarily have to be ceiling speakers.  They can also be mounted above your main speakers in the front top corners for left/right height.  The configuration is adjustable. 

Also, if you have a bluray that is Atmos or DTS:X, you can still play it through a normal HT processor.  Both of these formats are backward compatable on systems that only support DTS-MA and Dolby TrueHD.

If you know that you are only going to have a 5.1 or 7.1 system, then you don't necessarily need a modern processor.  However, if you think you might add more speakers in the future, it's better to get a Atmos/DTS:X processor now.

Thank you. I'm thinking I don't need Atmos, because I don't have overhead speakers, right? Which sounds formats are relevant for the 5.1 setup I do have? Thanks.

DTS:X and Dolby Atmos are the most you'll need.

The previou gen was DTS:Master Audio and Dolby Digital: TrueHD.