On top of your bottle purchase rental, all you really need is a regulator;
CO2 regulators (in the UK anyway) have a male thread, as opposed to most other bottles which have a female thread, so CO2 regulators are pretty specific. You should get a single stage single or twin guage unit, one the single guage unit, the guage shows the pressure output of the cylinder & on a twin guage the guages show output pressure & bottle pressure.
Be aware that the bottle pressure guage will not be of that much use to you, as the pressure in the CO2 bottle will remain relatively high until it is coming pretty close to running out, For this reason, if you can get a single guage regulator for less than a twin - go for the single. If you get the single, you can weigh the bottle when you get it & occasionally weigh it thereafter to get a better idea of what amount of CO2 you have left (remember to deduct the bottle weight though).
Other than the regulator, you will need a step down bush / reducer to allow you to connect your airbrush hose to the regulator & you will also need to find a method of securing the bottle to guarantee it doesn't fall over.
Other than that, remember that the bottle will contain a huge amount of potential energy & must be treated with respect (hence the bottle securing) & also remember that although CO2 is not toxic, it is an asphyxiant - so you must have adequate ventilation if you are using it for extended periods.
On the subject of your compressor, does it have a receiver fitted?
EDIT:- Sorry I forgot to mention price, a decent regulator should set you back about $70.