That should be all you need in order to use the paintball CO2 tanks. Not sure if you have a bubble counter, check valve, and diffuser but obviously you will need those.
In regards to the solenoid, does it come with the solenoid or will you have to buy a new one?
http://www.amazon.com/Huhushop-TM-Magnetic-Solenoid-Aquarium/dp/B00HIDNX6K/ref=sr_1_cc_1?s=aps&ie=UTF8&qid=1417331453&sr=1-1-catcorr&keywords=co2+solenoid+valveThat should work for your tank as well in regards to the solenoid valve if you happen to need one.
For tubing there is still a bit of controversy. If you use regular airline tubing the tubing will collapse overnight but most people say it doesn't have any sort of impact. Pretty much it collapses over night and then opens back up in the morning. I'm not sure if that causes any trouble over the long term. I wasn't sure so I just went with actual CO2 tubing. There is a big difference between regular airline tubing and CO2 tubing. The CO2 tubing is much harder and isn't anywhere near as flexible as regular airline tubing. I use the Aquatek tubing and it has worked really well for me.
For the diffuser it really depends on the set up. Most people go with either an inline diffuser or a ceramic disk diffuser. If you have a sump then you want to go with an inline diffuser since they have a higher percentage of diffusion than a ceramic disk. Atomic diffusers are fantastic and produce a very fine mist which is great.
Bubble counters are great since they give you an easy way to measure how much CO2 you are adding into your tank.
Needle valves. These are very basic but VERY important. If you do not already have a needle valve on the regulator, you will need one. Off the top of my head I can't remember which one is typically recommended but you will need a needle valve in order to dial in the right amount of CO2. Do NOT try to skimp on the needle valve. The one I'm thinking of is around $30 USD and they are very worth it. I hate my current needle valve but I've gotten it to work so no need to change it just yet.
Pretty sure that's everything so here is a quick summary. The adapter link is listed above and so is a link to a solenoid if you don't already have one (you need one). If you have a sump/canister then check out inline diffusers or else just go with a ceramic diffusers. Tubing is a personal preference, I've heard people use regular airline tubing and actual CO2 tubing and have good results. Get a good needle valve and don't try to skimp there.