You said you were looking for a "good" bass. Therefore,
do not go with Squier. On the other hand, just about any sort of Fender bass is bound to be good... at least in my opinion. Their P-basses and Jazz basses are prety sweet and simple. If you want to deviate from middle of the road, then Ibanez has some pretty crazy basses in its top of the line area. Epiphone`s basses seem like nothing too special, but they get the job done.
About what to stay away from, steer clear from Rogue and Dean. You may want to be wary of Washburn, but my main beef with them is that it`s the brand that all the "guitarists" use that know exclusivly power chords, except for those who are privilaged enough to nab a Fender. But remember, there`s no better judge of what to buy than yourself going into a music shop and trying the gear for yourself.
About sining and bassing simultaniously, I can`t help you there. I`ve tried it and it`s never worked for me.... but don`t be discouraged!