Here are some tips to help you find a good bass at the store or used from an individual.
If you buy from an online source you will not get an opportunity for personal inspection. Having said that, I have purchased some very nice instruments via eBay and it has worked out well. Just keep in mind that eBay sourced instruments often have some minor problems. I have the skills to fix most problems so it is not a big risk for me. If you don't have those skills you might end up having to take the eBay bass to a luthier for adjustments or repair. You may still get a great deal but it won't be quite as good had you received one not needing any work.
I don't want to discourage eBay purchases, I buy via eBay. Just be aware that it is possible to buy someone Else's problem.
A used bass with quality parts is the way to get good value.
If possible, get a used bass that includes a hard case. That will be a big savings.
Body - Tone woods are a personal choice, Alder, Ash, Mahogany, Maple, are all good. Each has a different sound so you need to study and gain some experience. Exotic woods are nice too but are probably beyond the budget. Avoid plywood bodies, if you can't get a description of the wood(s) in the body, pass, it might be plywood under a thick layer of finish. Basswood and Poplar are preferred by some players but are too soft, in my opinion. Tonewoods is not a science, some will sound great, others not.
Electronics Quality is important. I like Bartolini P/U's, but if you like the lo-fi vintage sound most will be OK as it is in the higher frequencies that the more expensive P/U's excel.
I think that a
pickup in the bridge position is important.
The John East Retro preamp is fantastic for fretless. Essential if you can afford it.
It's all about the neck!!!! If a bass has a good neck, that's a huge plus. The neck needs to be capable of adjusting to almost, or even actually straight. Too much relief equals no Mwah. When you audition a bass be sure to pay particular attention to the neck. The first thing to check is the relief, press a string down at the first position (equivalent to 1st fret) and also and the highest position. The depressed string is a straight line and the fingerboard is usually somewhat curved (relief). In the middle of the span will be an area of maximum gap, this is where you measure the relief. If relief is excessive a couple of things need to be checked: A. Will the tension rod(s) allow this neck to be adjusted for less relief. B. Is there a problem with this neck that caused someone to leave it in this maladjusted condition. I would not pay good money for a bass with excessive relief until it has been adjusted to be almost flat and the neck checks out OK in other respects. Check the straightness of the fingerboard. A precision straightedge is the best tool but your eyes can reveal major problems. Sight down the fingerboard and look for problems such as an uneven curve in the relief, an "S" bend (bad), high spots. If the fingerboard is uncoated minor defects can be corrected but if it's coated then the repair will destroy the coating requiring a re-coat. A properly set-up fretless bass should be easy to play in terms of the amount of mechanical force needed to get a note.
There is a lot of force put on the neck from string tension, narrow and/or slim profile necks tend to acquire/develop more problems than solidly built "hefty" necks. Just because a neck is built strongly does not mean it is not an elegant, fast, and smooth playing neck. Just be very careful to fully inspect any bass with a narrow nut AND a slim profile.
Ergonomics - One thing that might extend the period of time that you remain in love with your new bass is to make sure it conforms to the ergonomic dimensions you prefer.
For me, it's the string spacing at the bridge, and scale length. I like 19mm (3/4") string spacing, and a 889mm (35 inch) scale length vs. 864mm (34 inch) for Fender.
The 19mm string spacing is the standard Fender four string dimension, this spacing enables consistent right hand technique. If you what to slap this is very important. Six string basses are difficult to obtain with this width bridge, however the 90's vintage made in Japan Yamaha TRB 6II has both 19mm spacing and 889mm scale.
The 34 inch (864mm) Fender compatible scale length is the standard of the industry. This is a good scale, I prefer the longer 35 inch (889mm) scale because it has greater string tension which equates to more timbre from the string, so it's about tone. Low B strings especially benefit from the longer scale. In my opinion, short scale basses are not a good thing, although some people love them. Alembic has made the short (or medium) scale instrument one of their special lines.
A third important dimension (and more personal) is the width at the nut. Personally, I like a wide nut. I don't have big hands so it's not totally an ergonomic issue, a wide nut provides more wood at the weakest portion of the neck, transfers vibration better and (IMO) helps with solid tone.
Hang balance is important too, a neck heavy instrument gets old quickly. It is important that you try out your prospective bass with a strap while standing. Take your left hand away from the neck, if the headstock dives for the floor, it would be a good idea to look at other basses.
Before you pay your money, be sure that the ergonomics of the prospective bass will suit you for years. If not, then the quest for a great bass continues.
Strings - Strings for the 34 inch scale are less expensive and easier to obtain. I like a string that provides a complex character with lots of overtones. You can always cut the overtones out with EQ, but they can't be added if they are not there in the first place.
Roundwounds (I like nickle) are great if you have a fingerboard impervious to damage. If the fingerboard is wood I would go with a groundwound, pressurewound, or flats to preserve the wood.
RotoSound 77's , GHS Brite Flats, D'Addario Half Rounds, are all good (IMHO).
LaBella makes a nice flatwound.
Lots of good info on bass strings here:
http://www.juststrings.com/electricbassguitar.html
Some bassists swear by the Thomastic low tension strings. Personally, I prefer standard tension.