Pro-ject vs Rega

You bring in a variable (an included cartridge) that makes it all hard to answer. In general, I would prefer Rega over Pro-Ject for the table/arm combo.* Picking a cartridge is another question, and getting a good deal because it is included isn’t necessarily the way to good sound. Better to buy the best table, then buy the best cartridge in your budget and fit it yourself, as it isn’t hard to do.

*Yep, I just did the same thing by lumping in the table with the arm. But at this budget, that doesn’t really apply.

So Which cartridge you suggest? I know that Rega sounds best with their own cartridges 

I know that Rega sounds best with their own cartridges 

And how would you know that? They couldn't sound better with the best cartridges around (whatever 'best' means)?

I rebooted my vinyl life with a Planar 3, RB300 arm and a Shure V15xMR some 15 years ago. Then I changed up to a couple of BenzMicro MCs and then the Decca Jubillee and Reference. At that point I went to an SME table and so it goes. I have never heard a Rega branded cartridge, but I don't know of any reason to think they are as good as it gets. Even today, I have two RB330 arms holding extra cartridges on my SME tables. One of them has the best ever 'cheap' cartridge I have come across, the Nagaoka MP-500. It's good enough that I have already got two spare styli in the cupboard so I can keep it going. There are many other choices, and the fact is that if you like playing records you will soon have several.

I stand by my statement that included cartridges may be cheaper, but probably have little to do with 'best.' It is very easy to change a cartridge and align it well enough with respect to overhang, VTF and VTA that no one should be afraid to try. Please don't feel limited to Rega cartridges if you buy a Rega table.

I put an AT-ART9XI cartridge on my P6 replacing the Ania MC and it was a big upgrade.  I didn't shim the tonearm to adjust for VTA.  

Since you like warm, smooth sound I would consider the Planar 6/ Exact combo if you can swing it.  Furthermore, I am not sure the Planar 3 can get the most out of the Ania cartridge.