As mentioned from other reply, one style is not inherently "better" than the other style. A quality example of either style will have its own merits and drawbacks. The key is to get a good quality table, regardless of the style.
I really don't think you can go wrong with the belt drive tables that you mentioned. The person that said that direct drive is the way to go, what is their history / experience with turntables? Turntables and DJs from the club / professional scene? That field (especially mixing and scratching) really needs a direct drive TT due to the ability to quickly get back up to the proper speed, and they tend to be more durable too.
Direct drive TTs have the possibility that noise or rumble from the motor can get coupled to the stylus, and thus to the amp and output to the speakers. Belt drive tables have the motor decoupled to the platter and stylus by the rubber belt, so it really limits the motor noise that could POSSIBLY get to the speakers. But, a well-designed direct drive table (like the Technics SL1200) is just as good at eliminating motor noise as any belt drive.
So, I think you would be happy with the ones you mentioned. If you want to go direct drive, then I highly recommend the Technics SL-1200. It's built like a tank and does not suffer the motor noise problems that can be associated with other direct drives. This was the standard turntable for almost 40 years!
Of course, you will have a few people on here try to steer you away from the SL-1200 since it is a "pro" TT, but that is really a useless argument.
But, here is the real problem---They stopped making them about 3 years ago. So you have to go used or pay a big premium for new, probably more than double your budget.
But, if you don't mind used, then Guitar Center would be a good place to look.