Polly I was with orange on payg and you could top that up at a money machine, so I would expect all other phone companies to be the same. You can do this as often as you please, no time limits.
I understand that 3 do some good deals, never heard of giff gaff, but if Mick recommends it, it must be sound.
Why not go to Carphone Warehouse and ask your questions, they are supposed to be independant and have all the phone companies offers and will advise you accordingly,