Thanks again for all the info people! There is a LOT of good stuff in here, and it just keeps coming!
Now, a question...
I know it probably depends on what genre you're personally going for, but can anyone suggest simple(ish) songs that they first learned to sing & play? Surely there must be a few tunes that helped you bust through the "playing while singing" barrier.
I get the whole practice, practice, practice concept, but surely some of you guys have a "baby steps" song for me to try to sing & play?
Thanks!
Like @Joe Nerve said, it depends on your range - is there a popular song you like to sing along to when it comes on the radio/whatever? Start with that. If it's comfortable for your vocal range, do that. Also start listening to harmonies in songs and see how you can pick out those. If you're joining an established band, they probably already have a good lead vocalist, what they'll really want is a backup singer and, at most, someone who can change things up by singing lead once per night or maybe per set.
The tunes that I tend to take lead on in cover band settings (not counting my now-defunct alt/indie cover band that I did 2/3 of the leads on) are Love Me Two Times (Doors), Take Me to the River (Talking Heads), and the male (Fred) part in Love Shack (B-52s) - that last one isn't really singing, it's more what theater people used to call "talking on pitch." They all have pretty simple, repetitive bass parts that are easy to sing over.
You've had plenty of sound advice, so I won't pile on with generalities, but I'll add a couple of things. One is a bit of wisdom someone on TB quoted a while back: "The sad fact is that a good bassist can always find a band, but the really good bands don't usually need a bassist." It would be great to find an established band that happens to be looking for a bassist like you, but there IS a food chain to local bands and the acts at the top wont necessarily have an opening right now. If you do know one, awesome.
But if your experience is like mine, you'll probably be spending some time trying out with craigslist bands that may play a gig or three and then fizzle or whatever. I would say, that's OK - play with them anyway. Make contacts, cultivate the best people (most serious, good at getting gigs, play well) as ongoing connections, and don't be shy about moving up the food chain. You don't have be a jerk about that last bit, don't burn any bridges, but don't turn down good opportunities.
Where I've wound up, that I'm very happy with, is not so much "being in a band" as being part of a little network of musicians that always have various projects going on with different mix-and-match of people. For instance: a few years ago I joined a rockabilly startup. We played one gig and then the guitarist had a meltdown and I quit, not worth his drama. But the singer was great, and he asked me to sub in a Blues Bros. tribute he's in when the regular bassist couldn't make it.
Later on another group I was playing with had a singer quit and I asked him if he wanted to join, which he did, and then it turned out that the Blues Bros. tribute really needed a new core rhythm section, so we all learned that repertoire and I became the first-call bassist for that...
The group I asked him to sing for was Granite State Rhythm section, which was started by a drummer who had played with me in Six Cowards for a while, and we had also done some originals... he had fired GSR's original singer, who then went on to form a hard rock bar band with GSR's guitarist and a different drummer, and when THEIR original bassist left they invited me to join, so I wound up in Mugshot Monday... and so on and so on. You get the idea - form relationships, build a network, and different projects with gigging opportunities start to arise naturally.
The last thing would be repertoire. Go on auditions and you'll see what people are playing, all the regular stuff will start cropping up, Mustang Sally and Summer of 69 and Sweet Home Alabama, Keep Your Hands to Yourself, all that stuff. Apart from that, google the DJ's lists of the 200 top requested songs last year and go through it for anything that could actually be played by a band (a lot will be electro/pop/hip hop stuff that couldn't be, of course). Those kinds of things are usually a good bet to show up in cover band set lists.