The Rega P3-24 was made from 2006 until I think 2011, when it was replaced by the very similar RP3. Both are reiterations of the original Planar 3, and collectively are the essential mainstream Rega, possibly the best-selling family of budget audiophile 'tables of all time.
I used the Dynavector 10X5 high-output moving-coil cartridge, another mainstream star. At $450 new it's probably a little too pricey to be called budget—on a budget I'd go (for sure) with Shure M97 in whatever flavor is current. It is a hair shirt in that it is an utter PITA to mount and align, but I'm not sure I don't actually like its sound more than some much more expensivo carts.
If you own any Rega, run, do not walk, to buy a Funk Firm Achromat. My theory is that Britain is humid, and that's why Rega has stuck—and I use that word advisedly—with that horrid felt platter mat all these years. No one at Rega or associated with Rega has ever actually used the poxy thing in a dry climate, when it gets soaked with static and clings to vinyl like a vengeful limpet. The Achromat, which costs $115 in the Rega-appropriate 3mm variant, will make a bigger improvement in the sound of a Rega than any other tweak I'm aware of.
Funk also makes a whole platter out of the same stuff, calling it the Achroplat II. Do be aware that the Funk Firm has a somewhat dicey rep when it comes to shipping product in what might be known as timely fashion. You're on your own there.
Frank Smillie's gorgeously machined Groovetracer Reference subplatter replaces the cheap molded polycarbonate one that comes with the deck.
Whatever you do, do not replace the glass platter on a Rega with an acrylic one. You will make it sound like a VPI, and then you will have to shoot self. The Funk platter we will allow, since unlike an acrylic platter it does not murder all that is good and holy about the Rega sound.
The mandatory power supply unit (TT PSU—this is the old style of cosmetics), once hooked up, is what you use to turn the 'table on and off. And to change speeds. (Which, prior to buying this, you did by removing the platter and reseating the belt on a different part of the motor spindle.) And once you do that, you don't need the switch on the 'table and you're free to replace the plinth with a custom one such as one of Joel Scilley's Audiowood plinths if you want.
For toppings, try a TT Weights lightweight aluminum locking record clamp. You don't want to use a heavy weight on a Rega. The TTW makes no difference at all to the sound of the 'table, at least that I can discern on my vintage system in the basement, but it's lovely to look at as it spins.
I had intended to replace the bone stock arm with an Origin Live Zephyr, but by this time the turntable sounded so good I sort of lost motivation. Besides, I never finish anything.
Another tweak that benefits the Rega greatly is an isolation base, which you can very efficiently make at home by piling up appropriately-sized squares of unlike materials. Foam, plywood, bubble wrap, Formica—you can get creative. It's delightful to hear the 'table with all the ground-borne vibrations filtered out.
I sold this whole rig yesterday for $950, which is less than I had in the mods. But I had a lot of fun with it, and that's the category it falls into in the budget. It's all good. My deal is that I only listen to vinyl when I play pool, and it's much better to have a semi-automatic turntable (i.e., one that lifts the arm and turns the motor off automatically at the end of a record). I'm now using a vintage Japanese direct-drive semi-auto, so it was time to let the Rega fly away.