Cool. Never seen Red Dwarf.
The only reason I know it is because of this board. Never seen a frame beyond gifs.
You'd be in for a treat! It's influenced in part by "The Hitchhiker's Guide to the Galaxy" involving certain aspects, but RD clearly does its own thing instead and there's no real direct parallel, only the occasional aura. Mostly due to the dry nature of some of the jokes. Yeah, it could be described as "THHGTTG on acid".
I might have a suggestion, which may seem odd, but then again a lot of my posts seem odd so this one will be less odd by comparison... or more, depending on what qualifies as "odd", apart from me but I'm getting into recursive tautology and I digress:
Start with series two and move forward in sequential order. Some people do dare to slog through series 1, which isn't
bad, but as series 2 (commissioned via technicality, fortunately!) starts every episode with a basic premise recap so there is no real continuity, only something for anyone new to the series to understand the gist of so they can get right to the good stuff.
Continue from series 2 sequentially through series 6, then go back to do series 1.
From there, I can only say that series 7 through 9 are different beasts, often experimental, and the most robust format of the show wouldn't return until series 10.
You might want to try series 7's opener, which started years after 6's ended - if you don't like the tone, then maybe skipping to season 7's 2-part finale as it ultimately sets up the format for series 8. Series 8 - which IMHO is better, but not perfect. Series 9 was made ten
years after 8 was, is decent, but good enough at the time to warrant a proper renewal for the fairly glorious series 10 - present. Any episode skipped can be returned to; at the time I kept watching but some people didn't.

It's hard to gauge interest, but if you have the stamina and dexterity, doing them all in order but skipping to the next series if an episode feels so awful...
I forgot to mention, Red Dwarf does its own mini-reboots. Series 2 is almost a reboot. Series 3 is and that's when everyone says the show got big. Series 5 is also a minor reboot. Series 6 is a big reboot. Series 7's is huge. Series 8 tries to go back to basics. 9 is its own thing. 10 takes the best of all the different styles and perfects them all. Even the crap ones.
If you do want to watch in order, maybe the first two episodes of series 1 then move on. The others are okay, but they're not really needed as they don't add much to future continuity. Rarely is there any and, yep, the mini-reboots will change stuff too. Especially between 5 and 6 when they attempted to make the show in the USA. The DVD features on that debacle are a must-see. They chose the right people for the job, especially if you're a fan of a certain Dan Fielding, Harold T Stone, Roz Russell, et al... but the right production people can't guarantee a workable translation either. A bit of a shame, some of the new jokes worked wonders. Others didn't. Loved both Cat characters. Am I digressing on a digression's digression from the other digression again? Oops...
From memory, episodes from the (IMHO) least-effective seasons include:
Future Echoes
Waiting for God
Tikka to Ride
Blue
Beyond a Joke (this episode has Don Henderson's final role. A great performance already, it's made even more amazing when you realize he was suffering from throat cancer at the time... he did do some great villain roles...)
Epideme/Nanarchy
Cassandra
Krytie TV
Only the Good
The others from 1, 7 and 8 are "there" and might do more for you. The making-of documentaries go into some of the behind-the-scenes turmoil as well.