I've shot a LOTof deer with .22cf's.
Most have been on culling/depredation hunts.
I've used a .22Hornet to take over 50.
I've taken close to 100 with the .223, and a half-dozen with the .22-250.
With a .223, Any decent 55gr Soft-Point is going to work well.
Most of the deer that I've shot have been with the Hornady bulk-packed 55gr Soft Points with the cannulure. These aren't typically as accurate as the non-cannulure bullets and as such as shot placement is important, I prefer the non-cannulure.
I've had better performance from the Hornady 60gr PtSpt. This is what I've got now. I bought 1,000 "Blems" that MidwayUSA had several years ago. They have cannulures that were put in the "wrong" place and some only a rudimentary cannulure at that. (They were "blems" after all). They shoot well (about 1moa) from either of my .223's and .22-250 that has a 1/14" twist bbl.
I've also used 63gr Sierra SemiPtSpt and 65gr GameKings. I consider the 65gr GameKing to be the best deer bullet I've used in the .223 followed closely by the 63gr. These give performance similar to the .243 with a 100gr bullet...
I've not been tempted to try the Barnes, Bergers, or Nosler 60gr Partition as I don't feel this level of expense or performance is needed for our "smallish" deer. If I was hunting larger deer such as muley's or Canadian whitetails that run upward of 300lbs, I wouldn't even consider using a .22cf. But, for 100-150lb deer, the 55gr SoftPt's work just fine.
Just put them where you'd shoot a deer with a .243 or .25/06 and expect to find a dead deer.
Shoot them in the guts or blow off an antler, and they'll run just as far as if you'd hit them the same place with a .30/30....
With a .22cf or a 12ga or 45/70; the name of the game is shot placement, shot placement, shot placement.
I once shot a smallish 8pt buck with a 60gr Hornady Spt over 26.5gr of BLC2 from a 14.5"bbl Bushmaster AR-15. Range was ~25yds and deer was facing me in an "alert" posture with head turned slightly. I hit him in the neck and bullet broke the spine and exited. The bullet re-entered the deer through the hip and broke the femur and exited the ham near the base of the tail. Impact velocity was estimated at ~2,650fps. Total penetration was ~20" of deer.
Adequate performance....
Avoid the TNT's, Blitz, SX and such, likewise any HP. Also, FMJ's as they besides likely being illegal, also probably won't expand at long range.