Choosing a gaming laptop that affordable?

Affordable is a relative term. You didn't say what was affordable to you.

Anyway, an entry level game machine, such as the Lenovo Y510p, will run you a minimum of $750. A gaming laptop with okay performance will cost you between$1000 and $1250. A gaming laptop with good to great performance will run you from $1500 up to a solid $3k.

To go any lower in price would require purchasing a gaming machine from3+ years ago. If you want relatively cheap gaming hardware, you have to go for a desktop.

A gaming laptop you can afford? In the first place there aren't many gaming laptops. Very few laptops have a dedicated GPU and the ones that do are very expensive.
If you are an American expect to shell out about $1500 for one

Are you in the UK?
This is the best deal I could find:
http://www.medion.com/gb/prod/MEDION+The+Touch+300+Laptop+S6615+%28MD98455%29/30016631A1
Nvidia 745m.
Get a 750m or an 850m or better if you can afford it.