Squier is a company now owned by Fender. Previously Squier was the only company ever licensed to make exact copies of Fender bodies and headstocks. The components are not as high of quality as the MIJ, MIM, or USA Fenders, but you are essentially getting a bread and butter version of the Fender design when you get a Squier. Most of the ones I have heard sound fine. Things like the tuners, frets, bridge components, and pickups might not last as long or deliver like the more expensive Fenders, but the design is the most important determinant of the sound, and you tried them side by side so you know the difference. The bridge will be just as adjustable as a Fender, the neck can be adjusted with a truss rod, and the playability can be as good as any Fender style bass out there. Beginners are really lucky these days. Back in the 70's Squiers were more expensive than they are now! And the quality is better now, too. I think the body wood may also be different (poplar I think), but what you hear is largely the same. Poplar is not as heavy nor as hard as Ash or Alder. Cosmetically, you need to be more careful because bumping a poplar instrument could go past the paint into the wood pretty easily. Ash or Alder is much, much harder to do severe damage to. But this is a musical instrument and you need to be careful handling it anyway. Sound-wise, there might be some slight differences in these woods, but poplar has been used in many musical instruments historically and is a good body wood, even if it is not as durable and dense as Ash or Alder. If you are a little patient and look in the classifieds there will be something used. Squier is not a bad choice at all, IMO.
[Edit: I would not recommend against the Yamahas or Ibanez basses either. These are well made instruments also. Unfortunately what was posted about GC is apparently all too true. But at least they will let you play the instruments. Make it a point to visit as many dealers as there are in your area. Remember to shop often and buy only once. ]