Portable gaming laptop advice.

Hey guys first of all sorry for any lack of links in this thread but I'm on my phone.

I've been thinking of buying a laptop for a while and I might just pull the trigger on the purchase some time this week. I just thought I'd come here for some last minute advice. Here are my needs.

Budget: No strict budget as such but I don't want to spend an unnecessary amount of money. Say 300-400 gbp for the laptop and probably 100 on a bag, mouse and ssd.

Musts: It must have a good battery life, 3+ hours of moderate-heavy use is ideal.
It must have semi decent graphics as I'll play a few games but nothing crazy and I'm happy to lower settings.

Wants: I would prefer something small, 12-13 inches ideally.
I like the look of some of the Samsung and Lenovo laptops but the brand isn't important

I don't something crazy powerful, most of the programs I run would be fine on a Pentium 4. It's just to run a basic drum sampling program and play a few old games on long train journeys and when I visit friends and relatives.

I was thinking about an 11.6'' Samsung laptop with an e-450 and 4gb then upgrade the RAM because the graphics memory is shared and get a 64/128gb Samsung ssd because they have low power consumption and are reliable. The laptop is 330 gbp.

Any other ideas?