With some character types, such as Killer, there isn't any starting Martial Arts.
if a player were to take the character type without any Martial Arts and then later decided they needed to hit someone rather than shoot someone am I right in thinking that this would go off their Agility - 3 - so an unmodified character type of the Killer would be a martial arts of 2?
I realise this can be bought up, even at character creation, I just want to make sure I'm getting it right. It's been awhile since I've played and I'm also still trying to get my head around stunts and combat too.
You've got it about right- although strictly speaking you can't by italic skills at chargen.
I run it pretty strictly, because it adds a little variety and challenge for some types (Killer, Journalist, etc.) if they have to come up with other means to get over walls or between dangerous gantries.
You can be generous when it comes to interpreting the scope of Guns liberally, though- if someone wants to slide down a bannister and grab a gun from the table, I'm happy to let it be a Guns check because, well, it involves a gun and is the sort of thing guns-based characters do in films.
So if you were to raise the agility to 7 and then minus 3 for unskilled the Killer would be able to hit someone with their fist with an unskilled martial arts value of 4?
If they were to use a Gung-Fu type attack (like in Equilibrium) and use their gun as a hand to hand weapon would this instead go of the Guns skill?
Yes- raising Agility would be the only way to get a (slightly) better Martial Arts AV at character creation going strictly by the rules.
Using Guns as hand to hand weapons is something of a grey area, and depends on your taste. There are some house schticks that let you use your Guns skill in such a way- if you're allowing them in your game you probably want to restrict it to characters that have the schtick. It's a matter of taste and tone, really. Guns-based characters have no real penalty for being toe-to-toe with someone when trying to shoot them, so if they clobber them with the gun instead of pulling the trigger, that's really just flavour. On the other hand, you absolutely definitely want to make sure that you can't do anything fancy like acrobatics, or something that duplicates Fu schticks (like stealing a gun out of an enemy's hands) just with the Guns skill, as then there would be no point in picking up Martial Arts later on.