Welcome
I haven't any or much experience with Spyders purely because there are other more trusted brands out there that people use (Planet Eclipse), I think the more you play the better the paintball gun you will want, but for now just try out that Spyder to see how far you want to play paintball. There are other markers out there specifically aimed towards Woodsball or Sup'air balll (tournament paintball played on flat fields and evenly spaced bunkers), whatever you choose to take up will be usually decided on the type of paintball you want to take up.
Air tanks are usually either 48ci (0.8L) and 68ci (1.1L), obviously the bigger the tank the more paint you'll be able to fire. They are commonly constructed from steel (you will grow out of one of these very fast if you get one as they weigh a ton, and ain't very 'pimp') and fibre wrapped tanks which require a test every 5Years from its born date or last test date. The tanks in the for sale section here is most likely the cheapest place to buy one. One thing that you should take into consideration is weather the paintball site you will be going to uses Air or CO2, air tanks cannot be used to fill up with CO2 and vice versa. CO2 is more unstable as a mode of propulsion so many people would recommend you get air (still very much down to if the site you want to go to uses air).
I would highly recommend you get yourself a pair of good goggles, don't be cheap on them, as you want to have good vision and a highly comfortable set, look around and ask on here what people wear and why. Everyone is different so its up to you want you want to go with, just keep in mind that you can't buy safety, don't skimp on a tacky one. Again, there are many good sets of goggles on these forums for sale, most sellers are highly reputable, you can check by using their iTrader icons.
A good hopper will take you a long way, something to start you off would be a Halo or Vlocity, again from these forums as there cheap as chips and do the job just great (there just a bit outdated by other 'pimpier' stuff)
Good knee protection and elbow protection would be a personal recommendation of mine, by new, again, I don't skimp on safety as you only get 1 set of knees in your life, personal favs of mine are the planet eclipse paddings as they just provide great value for money in the amount of use you can get out of them for the investment you paid for them.
If you have any further questions feel free to post up (places other people play at, specific types of games, other equipment etc.), no1 bites here and everyone is a friendly face.