Compatibility? In what way? Sound, associated equipment, choice of tonearm? MC vs. MM? Output level? Loading adjustments? Active head amps vs. Passive step-ups? Solid-state vs. vacuum tube phono preamps? There could be an entire book written just about cartridge "compatibilty". Plus numerous disagreements in this forum.
Sorry for not being more specific. I meant for example, would I be able to put any cartridge onto my audio technica, or are some meant only for specific brands etc? Dumb question I know, but hey, gotta start somewhere
Which Audio-Technica turntable model do you have? Most carts are designed to fit a "standard 1/2 inch mount". That is usually a "standard 1/2 inch headshell". The AT LP120 has that type standard headshell. Some turntables have no headshell, or a different kind of headshell, but still use standard 1/2 inch mount carts. There were turntables that used only "P-mount" carts. Some carts were sold as "P-mount" only, and some "P-mount" carts came with an adapter to fit "standard 1/2" mounts". Some turntables have arms that fit only one exact specific kind of cart. The AT LP60 is one of these. You could replace that cart, if needed, with another cart of the exact same type. Many carts have a few different types of stylus available. With even the AT LP60, you can upgrade the stylus somewhat, somewhat better than the stylus it comes with.
Tone arms come in low mass, medium mass and heavy mass on TTs. Most cartridges are compatible with medium mass tone arms. Your Audio-Technica TT is likely equipped with a medium mass tone arm. For example, Grado prefer lower mass tone arms and Ortofon OM series prefer heavy tone arms for best tracking.
Unfortunately, that turntable comes with a fixed cartridge that can't be changed. According to what I googled up, it is a variant of Audio Technica AT3600L. All you can do is swap its stylus, which you ought to do after a couple hundred hours play. Make sure the stylus is one for said cartridge. Maybe it's a good idea to look for a used brand name turntable like Sony, Technics, Pioneer from the 1980s/90s. Most of those will be much better qualitywhise and will allow changing cartridges. In that domain there are only two groups of mounts: half-inch and p-mount aka T4P. All you need to know is what kind the tonearm of your new turntable accepts. Within each group, all cartridges are compatible with a given tonearm. However, styluses are not! A stylus is normally only compatible with one specific cartridge, or family of cartridges in some cases.
I wouldn't "upgrade" the stylus or cartridge on your ATLP60. The arm's tracking weight is factory set to about 3 grams, and that's what your stylus tracks at. A "better" stylus will probably track at 1-2 grams, meaning that the turntable would have to be opened up and the arm reset - not worth it IMO. Enjoy the AT60LP for what it is - a fun, secondary device that can play records...
A very good and unknown to audiophiles vintage TT is a JVC QL-5 or QL-A5. The 'A' series is semi automatic. It sounds unbelievably good & is inexpensive because it is unknown. It is also reliable with medium mass tone arm. Wow & flutter is less than .02% and is quiet at -78dB rumble. In my opinion it sounds better (specs better) than Technics SL-1200 series that cost $400+ and may not have a cartridge at that price. The JVC is about $150.
Agreed with @anorak2 and @allied333 with the suggestions. Other than the stylus, the LP60 has no meaningful upgrade options available as there is no mounting provision (i.e., 1/2" standard mount or a T4P type). Third-party higher quality styli has a tracking force range from 1.5 to 2.5 grams and since the LP60 is fixed to 3.5grams or higher from the factory (which is inconsistently built at the Hanpin OEM factory due to shoddy QC), it's far too much hassle to deal with the spring inside the player. In all honesty, I'd look into a better turntable from other companies like the U-Turn Orbit for something brand new. Used turntables as the two suggested are also great options.