I rent out resi dwellings so have looked into electric heating quite a lot. Budget, how long you intend to use the shed are factors too. In my experience, unless you live in a very upmarket area (South Manchester, Surrey etc ) future buyers/ renters of Houses don't pay much extra for nice touches like heated sheds, or good quality anything (taps, windows ...)
Questions
1 how often will you go into this on cold days. do you want year round heating, or just when you go in once a week ? Heat up times will be a factor for you if only occasional heating is required
2 are you cramming as many games in as you can, of will you have some "open space" on a wall
3 are you insulating it thoroughly (walls, roof, possibly even floor ?). If you will stay for years, I would use 2" of celotex, king span or equivalent on walls and ceiling. Expensive but very good
4 do remember that the easiest way to heat it, is of course just to turn all your games on if you will have a few in there
I would also consider whether you want a switch for the heating in the main house. If you are not heating it all the time, you will be able to turn on the power indoors before you go in
Underfloor heating is very tidy. But if the element fails, you have to dig the lot up so go for a big brand with decent guarantee that might actually still be in business should you need a warranty claim. It is by far the neatest and nicest way to do your shed. It takes a while to actually heat the room though so think about insulating the ground beneath the element. It relies on a relatively low heat, slowly heating the space above. So warm up time might be a factor
Good old fashioned wall mounted fan heaters are remarkably cheap, heat a space up quickly and do the job without using wall space where pins would go. They can look cheap, but in a cold outhouse do heat up quite quickly. I have one in my well insulated workshop, works really well
I actually like 3kw storage heaters if you want continuous heating (if you are already on economy 7), in well insulated spaces they work really well. And if 3kw they are a reasonable size and can be switched by individual timers. They would not be consuming power whilst you are playing. But it would need to go in a bit of open space (ie behind the door opening, below a window)