I was intending to bring up the whole truss rod thing but went off after other shiny things.
Definitely... if an otherwise awesome bass plays like a pig check the truss rod. It's of course important for guits but for bass (due to the longer neck) it can make a HUUUUUGE difference in playability. Also saddle height adjustments.
A lot of these economy basses you pickup at the music shops (and the guits too) have not been set up at ALL. Therefore a bass/guit that is otherwise really really nice might seem like a piece of garbage without a proper setup. That P-Bass I was talking about earlier actually suffered from that same problem. I had bought it used and I don't think the previous owner had the wherewithal to get it set up or do it themselves... and neither did I. It still worked great for what I was doing but it was a PIG to play. At one point after owning it for years a seriously hardcore bass nerd buddy of mine got his hands on it (we were about to go on tour and it was going to serve as the backup bass). He did a truss rod and saddle adjustment on it (and even fiddle with the nut a bit) and DAMN did that bass go from absolute PIG to playing like a dream.
Since then I've learned about truss rod adjustments and setting action/intonation and it's made my life much easier especially for studio work (where intonation becomes SUPER important due to all warts being exposed on "tape").
Point is... even if something is playing like a POS you may be holding a jewel in the rough simply due to the fact a lot of stringed instruments leave the factory floor without a second thought given to such matters (and why some stores will toss in "free" setups). Knowing the signs of an improperly set up instrument can end up getting you a better deal by way of the owner getting fed up with it without knowing how to set it up.
PS: If you intend to make truss rod adjustments though be VERY careful because that is one thing that can destroy an instrument. You push the rod too hard because you don't know what you are doing (or you are dealing with a neck that is actually WARPED instead of just an improperly set truss rod) you can actually snap the truss rod. Replacing a truss rod is a huge deal and likely only worth it for REALLY nice/expensive instruments.
Sorry... extra blathering. Hopefully useful in your search though.
PPS: Steinbergs are indeed cool but really.... they're expensive for good ones. I think you are correct in keeping it simple with the P/J Bass stuff. Then if you want to get all fancy later you can take your expereince with those models and figure out what you like better on the showroom floor.
Cheers.