Peavey Grind is about as good and cheap as a beginner could want.
Neck through so it has nice fret access, (as you are just starting you have no idea what kind of music you will be playing so get full 2 octive, 24 frets if you can).
Nice mono rail bridges that allow string through bridge or string through body, for different tones.
Also 2 passive soap bar style pickups that are very easily replaced if you find your in need of something more down the line.
I have a 6 string grind and I love it, even with much higher end instruments to play I find myself playing the grind a lot, I'm sure you will too.
The difference between cheap and expensive basses varies so much its irrelevant.
I like many here I'm sure have played some Squires that were better then some Fenders. Pretty much polar opposites on price but almost identical on features hardware etc.
This is no knock on Fender by the way, just a good example for how price is irrelevant. The days of getting what you pay for are for the most part gone.
ESP's are grand basses, make sure you look at the LTD versions as well.
Try everything you can, even if its out of your budget. You will be amazed how little price has to do with quality.
Pick something that feels comfortable (ignore and brands or prices) and you won't regret it.