My question is, can I pay off the remaining balance on the card every month so I am just paying the phone on a monthly basis, or if I pay a certain amount does it pay off the most least expensive purchases first?
In general:-
When making a payment, you'll pay off items charging the highest amount of interst first
If you have a £0 balance, and add a purchase, you get in the region of 50 days 'interest free' - i.e. if you make a purchase on day 1 of a billing statement, and pay it off before the statement due date, you won't pay any interest.
If you have a balance on the credit card, and add another purchase, you'll pay interest from day 0 - and keep paying interest until the entire balance is cleared.
Thus, with your 34.9% APR card, if you have the phone on there and add other purchases, even if you clear the rest every month, you will probably be paying interest on everything for the entire time the balance is there.
Note - check the detailed notes on your statement for the precise rules that apply to your card.
As others have said, a card with 34.9% APR would suggest that you do not have a good credit score and thus have never had credit before, or, managed it poorly. The best credit cards have rates below 10%, and something between 15-20% is pretty normal and achievable for people with a reasonable credit history.
As it seems to be the latter, then I'd look at getting a credit card with the bank you have your current account with - they'll have the best information to offer you a better rate on, given you've never had credit, and thus the credit reference agencies won't have much/anything to pass on.
In your circumstances, if I could only use a 34.9% credit card, and couldn't afford the phone outright, then I'd hold off and purchase it when I could - a sim only plan for a few months might give you enough saved up for it, depending on the price. Alternatively, there are schemes such as o2's refresh and Giffgaff that allow you to pay for phones over a number of installments at no/low interest - which should work out cheaper than paying interest on anything at 34.9%!
