There are lots of cards and options about so do look carefully.
Why, however, are you looking at a joint credit card? I am assuming that at the moment you are paying reasonably high interest rates on each of the 2 credit cards and so whatever you do you would be looking at ensuring you could move both balances onto cheaper rate cards. You best advantage would be to get 1 (or more) cards each ... and I don't think you can get shared credit cards - 1 person would have to be the principal card holder.
The answer will depend on just how high a debt £7k represents. If you get a 0% balance transfer this will have a limited life span and you may need to refinance this at the end of the free period. Not a problem if you have reduced the debt significantly by the end of the period, but a problem if you stll have £5k left at the end. You will risk not being able to refinance and stuck at a high interest rate again.
The safer option, my opinion, is to take a no fee transfer at a reasonable (6-7%) rate for the lifetime of the balance. Remember that the 0% option is NOT 0%; you have to account for the balance transfer fee. This is likely to be at least 2% so if the rate last for 12 months, then your APR is actually more than 2%. If the rate lasts for 9 months, it will be 3%+ ... getting comparable to the no fee lifetime balance rate. You other consideration is the monthly payment and whether you can afford it.
Be wary about cards that say 0% on balance transfers and purchases. Take GREAT care combining the 2. Generally they will offer the transfer at 0% for 12 months, and the purchases for, say, 3 or 6 months. Your payments will always go against the lowest interest rate first, and may even specifiy they go against balance transfers first before purchases. If transfer £5000, and spend £500 a month on your card (albeit at 0%), and pay £500 per month (to clear you purchases) then all your £500 payment may go against your balance transfer balance. After 6 months, therefore, your balance split will be £3000 purchases, and £2000 balance transfers. You will then start paying interest of 18% (say) on the £3k and (for another 6 months) 0% on the rapidily reducing £2k balance transfer pot.
Personally, I would take the balance transfer without fee at reasonable rate interest for lifetime balance. And use the cards you have paid off (make sure you get 1 months clear balance), for your purchases making sure you clear them in full. If you doubt you will be able to clear them in full every month (lets say a holiday payment crops up), make sure you use 1 card for the purchases you can clear off, and the other card for those you cannot. That way you will only pay interest on those purchases (holiday) thgat you cannot immediately clear.
I think that's enough advice for now!
