I had one of those SL-QD33s once, with an Ortofon cart (I think it was an OMP5). I thought it sounded pretty thin. I've also heard them with the ubiquitous AT "wedge" carts (AT90CD, 3472, etc -- there's a dozen or more variations on the lpgear page) and it wasn't any better.
My first choice would be an old Stanton, the L727, L737 or L747 if you can find and/or afford it. I haven't heard a Grado on that table, but I'd think it should perform okay. The main thing is you want a cartridge with some beef to the sound, because those tonearms really seem to need that.
If you want to go super-budget just to get the thing running, you could try the p-mount Red Ed, a.k.a. the Sanyo MG29P. Those can be had on eBay <$20 shipped. I've been pleasantly surprised by the standard 1/2" elliptical stylus version as a budget cart. Haven't heard the p-mounts, which come standard with the conical stylus.
Real name Nagaoka (the OE manufacturer) C501M/P
http://www.soundring.com.au/en/products/hi-fi-cartridges/c501m-p-moving-magnet-detail . However, sorry to be the bearer of bad news – it won’t be a good choice. The Nagaoka C501M/P has an ideal tracking weight of 1.8-2.3g. So the Nagaoka/Red Ed/Sanyo at 1.25g (the p-mount standard), will be tracking at well below what it’s designed for. Nagaoka attempted to adapt a cartridge that doesn’t have an ideal tracking weight of 1.25g to become a p-mount, by putting a p-mount body on it in place of the original half-inch mount body, and making no other changes.
I'm not sure what they were thinking.

I suspect the Nagaoka will really struggle at 1.25g, which most non-adjustable p-mount tonearms are set at. It works best at 2g as a half-inch mount cartridge (Nagaoka C51M/II/Denon DL-007/Red Ed/Fisher MG-29D/Goldring Elan/Kenwood V51/II/Music Hall Tracker/Sanyo MG-29D/Toshiba C51M/II) on a half-inch mount tonearm.
The Ortofon 310 (or for the same performance at a slightly higher price, the OMP 10) is probably a good choice, although it works best at 1.5g (according to Ortofon). It should be OK at the p-mount standard of 1.25g, though. It can also be upgraded later with a better stylus (Ortofon 320), if you have more money, as can the OMP series. An Ortofon OMP 10 with a stylus 40 would be good. There was also a 5x0(P) series, that some sellers still may have - the 510(P) would probably be the correct price, and can be upgraded all the way to 540(P) by changing the stylus. Like the OMP 40, the 540(P) has a nude Fritz Gyger 70 stylus, but it is rather pricey at some sellers...
Bear in mind, if you go for an Audio Technica cartridge (the other brand I'd recommend), for the best sound, they need to be loaded with a particularly low capacitance (150pF). Most turntables and amplifiers will supply a lot more than that, which may be why some people think Audio Technica's don't sound as good as they are capable of sounding....
For a really cheap p-mount cartridge, Shure's M92E (the current universal mount version, not the earlier version, which was half-inch mount) is quite OK. They (and the replacement styli) seem to be very widely available at reasonable prices, although how long that will be for, nobody knows. Let's hope they don't follow Stanton's lead and stop making any hi-fi cartridges and styli.