used is another way to go.  Sometimes you can find nice used equipment that is very nice.  I've always like Ibanez bases.  The cost vs. performance there is very good.  For a < $200 you can get a nice looking/nice sounding bass:
http://www.guitarcenter.com/Ibanez/GSRM20B-4-String-Electric-Bass-Guitar.gchttp://www.guitarcenter.com/Ibanez/GSRM20B-4-String-Electric-Bass-Guitar.gc
 
This doesn't have any active electronics, but the pickups should perform similar to a Jazz bass.
This one does though:
http://www.guitarcenter.com/Ibanez/GSR200-4-String-Electric-Bass-H75860.gc
 
Again recommend trying these before ordering.  They do feel different than the Fenders of old!
 

I have an old Ibanez Blazer Bass (bought in a pawn shop in Nashville).  It sounds and plays just like a P Bass (the pickups in it went bad and I replaced it with a set of Fender P-Bass pickups - an exact fit).  This model may even be part of the "lawsuit" guitars.

fireberd
The problem with some "not a big name brand" instruments is resale value.  You usually take a hit when trying to resell them (if you even can).

 
This- Sage advice-   As I said, if it's not made in USA or Canada it's just another import factory made axe and it is what it is. There are plenty of times these instruments are put together nice enough to be enjoyable to play. 
But one needs to know what a good instruments feels like first before trying the rest. 
My favorite Bass is a $199 Yamaha ( Indonesian)  I've had for 18 years now but I had to swap out the Pups to  DeMArzios to make it right. And that's what your not going to find on any cheap import,,, good PUP's. No big deal. If you like the way it plays and feels, pups are the easiest upgrade you can make on a Bass. 
For me a deciding factor is weight. That's why I love my Yammy, it's nice and light. I have an old Hondo that weighs 100lbs too and it's as good as any Fender but it cannot be worn for more than 15 minutes. I also have a Godin 5 string that is a bit to heavy to play all night. Awesome bass but will kill me. 

I personally own a Japanese (1974) Fender P Bass.  The pickups went out and I put in some EMGs.  The thing is sweet!
 

Johnny's point about PUPs is accurate. As long as you play a guitar (physically use it) and it is solid, made properly, and has a fully adjustable bridge, PUPs and wiring are the only real variable requiring "replacement"(and a fun playground for those who enjoy it). If it satisfies your creative needs, that is what matters most.

I have yet to sell any equipment and would never consider a guitar an investment, but realize there are some who consider this.

Absolutely digging the feedback!! I'd been considering looking into pickup replacements, but for a start I'm gonna take whatever I get and get good using that :) We've got a budget of about $375, part of which will be used on a nice case. We've got a decent amp at the moment (Fender Rumble 1x10) that works perfectly and gets plenty loud for our needs, so that's not getting an upgrade within the year.
 
So here are the three options I've currently got my sights set on:
http://www.guitarcenter.com/Yamaha/TRBX174EW-Mango-Wood-4-String-Electric-Bass-Guitar-Natural-1418660058856.gc?pfm=item_page.rr1%7CClickCP (I've always been a huge fan of Yamaha, two of my trombones and one of my trumpets are theirs. I can honestly say that my flugel, Holton trumpet and Olds trombone are *quite* as good in build quality as any of my Yamaha horns, so I trust them big time! Plus this is a really nice looking bass at a good price point.)
 
http://www.guitarcenter.com/Mitchell/MB300-Modern-Rock-Bass-with-Active-EQ.gc
Again, I liked how the 5-string felt, but I didn't realize it was on-sale at that time. If we settle on this guy, I'll definitely wait until the price comes back down.
 
http://www.guitarcenter.com/Squier/Bass.gc#narrowSideBar
This is just all of Guitar Center's Squiers, I haven't looked deeply into them but they seem to be raved about.
 
So how's this look? Anything stick out to you guys? It's helped in narrowing things down a LOT (even though that Squier list is still pretty big).
 
Thanks a lot! I'm getting closer to the final decision!
 
 

mettelus
Johnny's point about PUPs is accurate. As long as you play a guitar (physically use it) and it is solid, made properly, and has a fully adjustable bridge, PUPs and wiring are the only real variable requiring "replacement"(and a fun playground for those who enjoy it). If it satisfies your creative needs, that is what matters most.

I have yet to sell any equipment and would never consider a guitar an investment, but realize there are some who consider this.

Dead on, on both points.
I tend to buy MIM Fenders (3 of them at the moment), and replace the pickups.  To be even stingier, I buy USED MIM guitars and basses.  Then I've upgraded the pickups and bridges in all of them, and they sound and play better than anything else I've bought.  And all-in, probably $500 USD for each.
I also have a Yamaha TVL guitar.  Yamaha quality has really improved in the last decade!  
 
And like Mettelus says, i don't buy them for investment.  You've really got to get into high-end instruments before resale value would make a significant enough difference to be worth what you pay at buying time.
 
From the 3 links you gave, the Squier link didn't work for me.
Between the Yamaha and the Mitchell, they're very similar.  The Mitchell looks a bit nicer to me (i like the sunburst), but Yamaha is a known model which I expect will play nicely.  But since you've played a Mitchell and liked it, that may negate the playability.
At that low price-point, re-sale value shouldn't really matter.  You'll probably get 50% of the new price for either of those.

Slugbaby
From the 3 links you gave, the Squier link didn't work for me.
Between the Yamaha and the Mitchell, they're very similar.  The Mitchell looks a bit nicer to me (i like the sunburst), but Yamaha is a known model which I expect will play nicely.  But since you've played a Mitchell and liked it, that may negate the playability.
At that low price-point, re-sale value shouldn't really matter.  You'll probably get 50% of the new price for either of those.

Well it's all starting to speak for itself - and it did when I went to trying out basses in-shop - within this price-point, EVERYTHING that isn't bad is going to do just fine as long as it feels good and has pickups that fit the sound one's going for.
 
We'll most likely go for the Yamaha - I'm talking to my buddy from Germany who has a slightly older version of this model and he says the one he's got is good for the money. These days he's playing a 4- and 5-string Sandberg and loves those to death. 
 
Looking forward to getting more into this! I've always loved playing bass, but the more I play and research, the more I realise I DON'T know!

I've only seen Mitchell basses in GC and MucisionsFriend (which, I believe may be owned by the same parent company?). It's very possible GC has been struggling to find new brands that can quickly fill gaps in the mass-production market. I've picked up a few of them, and although the styling looks very 80's/90's, the sound isn't bad at all. They have some great-sounding pickups, and playability seems pretty good to me.

From perusing their Press Releases, they seem to be in the realm of Sire (Marcus Miller), but for different tones and styles. This is becoming a new thing with newcomers that are fraught with the history of shoddy instruments, which discourage new players from getting good. With today's CNC builds, it's far easier to get a high-quality instrument at a lower price than ever. Just go look at what you can custom order from Carvin. You can custom order a really sweet bass that luthiers would charge quadruple to build for you. 

I highly recommend plugging those in and A/B them to the new Fenders and MusicMan basses. They won't match perfectly, but you can at least stack them up to some of the most sought keystone basses in the market.

I've never heard of them myself either, but if it plays well and and feels good in your hands and to your ears, then play on with the Mitchell.
 
I use a Schecter Raiden Deluxe 4 string bass.  It's no longer in production, but I like using that bass.