350pounds is about €550
Mexican Fenders can be found new for that price (bought a Mex 5str two years ago for about €600, sold it for my MM fretless + Fenders' active electronics aren't all that).
OLP (seems to stand for Original Licensed Product

) is an ok MusicMan copy, active, maple or rosewood, 4 or 5 string.
Yamaha BB G4A/G5A,
BB405, BB G5S, ... all basses in your price range.. depends on your musical taste + playing style.
Ibanez ATK series, Warwick RockBass series, .. there's a big market out there.
"Keep away from active electronics. It's like driving a car without feeling the ground."
Yes and no, cheap bass=cheap electronics..
"rosewood neck if you want heavy sound or one with a maple neck if you like a more bright sound"
Maple is a harder type of wood so it will sound harder, more mid, sharper highs, while rosewood being softer will sound rounder ("warmer" anyone ?

), deeper bass,...
Herwig
personal favorites: musicman 5 fretted&fretless, ken smith 6