The simplest answer to "where to buy" is to do a Google search! Relatively few p-mounts are being made now, so the choice for new units is quite small.
Retailers like LP Gear in the US offer a good choice at most price levels.
When searching, don't forget to check out DJ retailers. DJs kept vinyl alive during the lean years after CD arrived, and retailers supporting them often stock Stanton and Shure cartridges, and may have a few p-mounts in stock.
There is also eBay! This is a good hunting ground for New-Old-Stock (NOS) cartridges. These are basically old cartridges that have never been used, and a number of the Demo files available here were recorded from NOS cartridges. It's worth checking Jico and other retailers of replacement stylii for the availability of styli for the cartridge you're planning to buy. This is even more important if you get hold of a used cartridge. An established eBay retailer is William Thakker, who sells new and NOS p-mounts and replacement styli. They also have an online store outside of eBay. It's worth checking both as stocks and prices may be slightly different.
Many turntables being sold on eBay come with their original cartridge, which is liable to be very worn or unusable. If a good replacement stylus is available it's worth putting a small bid in on the turntable just to get hold of the cartridge body. This was the source of the Technics P22 used in the Demo files with a Jico SAS stylus.
Occasionally you see a Technics moving coil (low output) p-mount for sale secondhand (EPS-310MC). These were the original fitting on decks such as the SL10, and were (are, if they still work) among the very best cartridges made. For this reason you need deep pockets to consider buying these, especially if they need a re-tip or new cantilever.
Sometimes you can get replacement styli for a range of cartridges where the original body is no longer available. For instance - an Ortofon OMP40 might not be available, but an OMP10 and a Stylus 40 is. Swap the Stylus 40 for the Stylus 10 in the OMP10 and you have one of Ortofon's best moving magnet cartridges (plus a back up needle!).
It's also worth checking out which other styli for a manufacturer can fit their other bodies. For example, a lowly Shure M92E can have a performance boost with a N110HE stylus, or a N97xE stylus. Google is definitely your friend here.
Internet forums are a good source of anecdotal evidence about which works with what, and Vinyl Engine should be your first port of call. They also a have a very useful cartridge database.
The choice of cartridge you make will obviously depend on your budget and what you're trying to achieve. If you only have a small budget, the cheaper (new) Audio Technica cartridges are great value for money. A NOS Shure M92E might also fit the bill.
If vinyl playback is going to feature more heavily in your music playing, then a better quality Ortofon OMP could be the solution, or one of the NOS cartridges featured on this site. Very limited supplies of the Ortofon X1-MCP (high output moving coil), for example, are still available. You can use the Demo files here to help you decide whether the sound quality is what you want.
It's worth saying, too, that with the more expensive cartridges, a properly maintained and serviced turntable will be needed to get the best out of them. With eBay prices for decks like the Technics SL7/10/QL1 (the high end of Technics linear tracking output in the 1980s) currently around 70-100 GBP, a similar sum spent on servicing them will produce a turntable that will outperform many a modern deck retailing at 1,000 GBP or more! Upgrade the power supply, bearing, better feet for isolation, more damping and maybe a better platter and you raise the bar even further. While the mega-expensive moving coil cartridges are ruled out for p-mount turntables, given the right deck and cartridge excellent results are possible.