Doing it at home requires a flll station of some sort. Standard compressors are no good, a scuba tank and adaptor are most common for those who do
However, you don't need that
Fills are free when you play, once you have your own cylinder either you fill it or the staff fill it. They are likely to have you self fill as staff will be covered for the site cylinders
Before you buy your own you can still use site cylinders, even if you buy your gear a bit at a time and have your own gun but their cylinder etc
(Obviously ask the specific site, if it's at an established site then 99% the time they will be there anyway, if it's an event run on the site by someone else or at a different venue then they would need notice)
Air or co2?
Air is preferable. Co2 should only be selected if it is a site that only runs co2. Co2 would restrict your choice of gun, and co2 only sites will be punter only.
Idealy you want to move on to walkons or events, both to see more of variety in paintball and to save you money compared to punter rates
(Search for the 'what paintball costs' thread which lists various kinds of paintball and the general cost)
Note that I have said walkons and events are cheaper than punter paintball, however when you check the costs thread you will discover that you get more for your money so unless you play limited paint will probably spend the same to play whether as a punter or walkon
Disposable co2 is an option, but only realy practical for things such as pistols using 12 gram co2 cartridges
Compressed air cylinders are the ideal choice. An aluminium 3000psi cylinder will suit most people and costs about £30
When you've got the feel for it consider a fibre wrapped 4500psi but before spending £150 on one get to know which will be right for you, they come in a variety of shapes and sizes
Depending on what you are looking for scenario and magfed are the closest to airsoft
Magfed if you fancy more 'realism' with limited shots per magazine etc, or scenario if you like the idea of a storyline and mission based games
The choices you have are vast. This year is my 10th in paintball, and in 10 years 1 week I achieved my goal of playing every form of paintball available in the UK
No matter what flavour of paintball, it's shooting people and getting shot at. Every kind is awesome in its own way
Welcome to paintball, enjoy