Bass guitar suggestions

Alright guys, so I'll be investing in a new bass next month to replace my Epiphone Thunderbird IV and I need your help. Basically, I'm looking at getting a Fender Precision but unfortunately that may be out of my price range so I may have to look elsewhere. I'm looking for a bass which can give me a really thick bass sound with barely any click and very little treble, but doesn't sound like complete mud. I know some people will say just go to the shop and check whatever out for yourself but I just wanted to know if you guys could help me with finding a bass which can achieve what I want.

True point, and if it helps I use a Marshall 300W Bass Amp so I'm not running it through something cheap. The Fender P is £450 at my local store and is pretty much the same price everywhere else online but I don't want to get it online seeing as for some people problems creep up such as dodgy action or other things.

Depending on a few different factors my budget could range from £250-£450. Some of those factors being how much I get when I sell my Thunderbird and how much money my girlfriend wants to give me for my birthday.

Yeah I'll be seeing how much money I get before I sell my Thunderbird but before that it would be cool to hear if some fellow bassists have any sweet recommendations.

Did I mention it was an Epiphone Thunderbird and not a Gibby? I'd be very surprised if I got £200 for it because it cost me £250.

And that seems to be the normal going rates for Precisions around here so I'm pretty chuffed if that's a good price.