The answer to your question is going to depend a lot on how much free money you have to work with on a monthly basis and what level of competition you want to reach. If you want to be competitive with the best of the best players on the F2P, you need to understand that doing so will be extremely expensive. The initial cost to reach competence with everyone else is going to be relatively high, on the order of ~$500. You are likely going to drop between $100 to $200 a month after that just to keep up and may very well spend more than that. Note that these costs aren't going to immediately put you on par, you are going to be spending this much over an extended period to slowly build up to the full level 12/13 runes and etc that the strongest players currently use. Even after you reach that point in a few years, you will still be likely spending over a hundred every month because of timed items running out their durations and to keep your premium level up.
The advantage of playing on the F2P is that all content is available to you and, last I checked, you'll be playing on a much, much more populated server. If the price I quoted is too high, the P2P server is an option and is... likely the better experience for a player overall, even if you will be missing out on a substantial amount of content restricted to certain premium items. The upside of that is everyone else will also be missing that content, so the barrier to reaching the top level of play is a LOT lower. However, the P2P server is likely going to be much less populated. Long ago when I played on the P2P server, it was also heavily timezone restricted as most of the player base was EU with very little population located in the NA timezone. So about the time I got off work, most people were finishing up their playtime for the day. You didn't have that problem with the F2P server.
What I would suggest is buying one of the available Collector's Editions that comes with some P2P time and checking out both servers. Get an idea for what the population level is like for both League and Empire factions at the time you would be typically playing the game. With that information and knowing what kind of budget you have for spending on a game every month, you should be able to pretty easily determine which server, if either, are right for you.