Welcome aboard. Nothing wrong with going for a GBB rifle of course, but if you are new to airsoft, I'll echo what others have said about it probably being wiser to go with an electric gun.
But, it's your money. Just be aware that AEGs are generally a hassle-free 'work straight out of the box solution', whereas GBB weapons can take a bit more TLC to get the best out of them, notably my GBB MP5K. To give you an example of some of the things you have to be aware of with GBBS, I bought three brand new MP5 GBB mags a couple of weeks ago for my MP5K, and all three of them needed the seals fixing upon arrival, not one of them would hold enough gas for more than aboutt three shots. Now to be fair, this is a reasonably common issue with large capacity MP5 GBB mags, so I was expecting they might need sorting even though I bought them new, and it's not that hard to fix when you know what you are doing and have the correct tools and such, but it is an example of the maintenance you sometimes have to get into with GBB weapons. AEGs on the other hand simply require you to remember to charge the battery. Then again, you might like the 'armourer' aspect of loking after guns, and if that is so, then don't let me or anyone else stop you from getting a GBB, although you do also need to be aware that their performance can be quite severely affected by temperature and air density.
Balancing against those more labour intensive aspects of GBBs, is the fact that they are more akin to real firearms in both action and operation, and in the fact that the 'firepower' is contained in the magazines rather than in the rifle, making changing mags a more satisfyingly realistic affair.
I'm sure if you have been playing CQB a bit, then you will already know a few of the plus and minus points of it. Notably that a quieter gun is a bonus, a shorter gun is also a bonus, and that whilst high magazine capacity is a bonus when in a close fight, the rattle which high cap mags make can give your position away. You are also far more likely to clang your gun into a wall in the close confines of CQB as oppsed to when outdoors, so metal barrels and flash hiders are also a bonus, as plastic tipped barrels and flash hiders can easily break.
With all that in mind, shortened carbine variants of the Armalite rifle, such as the M4 and AR15 are good CQB choices, as are shortened Kalashnikov rifles such as the AK74U, the U standing for Ukorochenny (shortened), as indeed are various MP5 variants, particularly the MP5K, the K standing for Kurz (short).
Having said that, pretty much any weapon with a folding or collapsible stock, or a weapon which is not overly long will do for CQB, including pistols, although if you like realism, don't use a G36 rifle with the stock folded for CQB, since the real G36 cannot be fired with the stock folded without damaging it, i.e. its folding stock is designed for storage purposes and to make it easier to get in and out of APCs. Anyway, back on pistols, you could also consider dual-wielding pistols, which might be kind of fun. Either way, a pistol is quite handy to have as a back up to your rifle, and is vastly more usable in really tight CQB spaces, so is absolutely worth considering, and, since GBB pistols are more common (and cheaper than rifles for the most part), this might feed your hunger for a GBB weapon even if you get an AEG rifle, i.e. you could get a GBB pistol and something like a G&G short M4 and probably stay within your 250 quid budget if you shop around a bit.
