You can't use 6/2 if you want to use it with a normal subpanel. If you are balking at the price of 6/3, we have an answer for that.
You can't use 8/3 because in NM and UF, it's only good for 40A.
I don't know why you want to use UF cable inside conduit,
"It's the devil I know"
... understandable. But the 6/3 UF you would actually need would require 2” conduit (really).
If the run is entirely inside conduit, or for the segments which are inside conduit, then meet a new devil: THWN or XHHW or USE. It is sold as single individual wires. Buy what you need.
If you like saving money, also, it comes in aluminum, which is fine for these large sizes, especially going to a subpanel, where the lugs are aluminum!
As a bonus, THWN and XHHW are allowed higher amps on the same size wire!
For 50A using THHN, XHHW or USE, you can use #8 copper or #6 aluminum for hots and neutral. Use #10Cu or #8Al for ground. You can mix and match.
Rigid Metal Conduit
RMC is a specific type of conduit that looks like heavy steel pipe for compressed air. Because a shovel strike won't even faze it, it is allowed to be buried with only 6" of cover.
It is threaded, and you should thread most of it, but they also make threadless couplers so you don't have to get into pipefitting for that last few feet that need to be precise.
However, it is hella expensive. As much as $3.00 a foot! depending on size.
If the conduit route is complete, you can use the shell for ground. But I wouldn't. #1 that only lasts until the pipe rusts out. #2 that means you can't switch to PVC conduit for the parts that are not underground. (You could switch to EMT, however; that can carry ground.)
The conduit must be assembled absolutely complete, backfilled, and tamped before ANY wires can be pulled into it. That means you need to build it properly so it can be pulled. No plumbing elbows! Access points must be built-in where they need to be (e.g. LB conduit bodies at the ends of the stub-ups).
