Most people recommend a G&G CM 16 as the best starter gun, I think it really depends on your preference. The Combat machines comes in many different M4 variants. If youre only 13 maybe some of the longer variants might be a bit to heavy for you. CYMA are a good brand for AK variants, another brand I recommend is ICS.
If you prefer AK's to M4's G&G make a "RK47" which I have heard is also a good gun for the money.
Another good gun is the KWA CQR, however its a bit over your budget around £160.
In terms of protection, as youre under 18 you will require full face however this does not mean you must wear a mask. I am over 18 however I think face protection is important, I wear a mesh mouth protector which protects my teeth from damage. Any ballistic rated eye protection should be fine, depends on your preference again I wear goggles because I can fit my glasses underneath them.
A variable some people overlook is footwear, if youre planning on playing at an outdoor site a good pair of boots is definitely recommended. So factor this into your budget