Welcome to GC. Hopefully you find it to be a fun challenge. This link can start you off with a lot of useful information:
http://gc.gamestotal.com/hef.cfm?f=hef_detail&hi=6223&ch=101
Major differences that you will notice are that there are no lords, OP, transports, big turn storage, systems, ministers, fast build, etc. The list goes on and on. I think you`ll find that GC is a bit more challenging in that it requires a great deal of independence both in and out of battle.
Another thing that should be pointed out is that, while there are no lords/vassals on GC, there are in fact slaves and masters. This is not to be confused with lords/vassals though! Enslavement means that while you are enslaved, a sizable portion of your income goes toward your slave master`s tribute box. Do not let people fool you by saying they can give you money as your master! The money that they can send is your own money that they took in slave tribute to begin with! If you do get enslaved (and this happens a lot with newer players) do not get angry or frustrated. Keep your cool and either try to break free or ask nicely to be let go. Believe it or not, some masters will let their slaves go if they ask nicely. If they don`t, stay chill. You can still break free by climbing to 10x their pr and declaring independence from the slave empires menu.
Another common issue with new players that you can find covered in my game guide is money. Starting out can be financially challenging on GC and many go into debt. A nice way to earn some quick cash is to mine and sell ore. This will get you started off nicely, but don`t rely on it as your main income forever. If you do end up going into debt, sell minerals, food, ore, raw material, etc that you don`t need. Disbanding any ships and not using turns are also good ideas for when you`re in debt.