that’s funny @PamPurrs and @Jazzbass19 , I myself am not really into a particular era. the music of my youth is mostly from the 90’s and 2000’s but I can’t say I prefer this era over another one. I like music from the very early ages of blues to the last week’s releases 
the most recent song I’ve covered has been released in december 2020.
funny how we all can have a different personnal relashionship with music.
I choose songs based on various principles. First my goal is to diversify so some of the songs I cover are purely songs I like. Others are songs I hear through my family and they say can you play such and such. Then there are the songs that I don’t listen to but hear a bass line and think I have got to see if I can play this. I really want to be well rounded in my playing style and employable so to speak. My end goal is to write jazz fusion songs
Currently its a mix of songs learnt in the lessons and the stuff I played air bass too as a teenager (and as a grown up when the misses is out) Now i’m doing the same thing but with an actual bass
I think that it is all down to subjective memories. i love the lion sleeps tonight(tight fit) but hate sailing!,(Rod Stewart) so my current challenge is David Bowies lets dance, just go with whats in your heart.
Only reason to cover any song, otherwise I can’t sing with power when I don’t feel the emotional attachment to a song. Which has become my standard, hence why I still have’t posted any covers. I’m not yet up that level.
When I chose to learn a song and look up the tab for it, I basically chose whatever song I find interesting at the time. Lately I’ve been looking into Oasis bass tabs. Nothing special but I love playing along to their records. I play a lot of punk rock, so simple basslines and simple guitar chords are too common for me.
But when I try to seriously cover a song, I always try to expand on what the original band made. For example with “Basket Case” by Green Day, I have the bass sticking to the root and third of the chords (a sort of back and forth motion; Mike Dirnt sticks to the roots and plays fills in between chord changes), while the guitar is instead played on an acoustic guitar using open chords. I also cover it as a duet. So basically I turn Basket Case into a folksy country song, but we still scream they lyrics as if we were being mauled by bears.
The challenge of a difficult bassline is really just trying to understand how it fits in the mix. I’m still a noobie bassist, so when I see a weird note in the tab I’m thinking, “Wait hold up, why is he playing that and when should I play it?” Then I end up having to listen to the recording and learning by ear, which is good practice ngl. The challenge of bass for me is trying to visualize a groove in my head, because I’m originally a guitarist so I naturally don’t have much groove 
, and this becomes apparent when I read tab. Thankfully, Josh has taught me how to read rhythm via sheet music and that is wayyy more helpful.
I choose songs mostly from my youth, I liked it when I was in my teens 40 yrs later I still like them. If I am trying to learn or practice a technique I may pick a song to work on that makes working the technique more fun and I have a benchmark. Learning slap I choose to learn Higher Ground, leaning into funk I am working on What Is Hip and my plucking speed and endurance keeping a steady beat is getting a work out. But mainly I think you have to like the songs, unless you’re in a band environment who bothers to learn songs they don’t like.