£165 is so cheap.
What about if it is bad weather? You won't go outside and run.
You can get a lift/drive/bus to the gym.
Secondly, weights will be a huge help in changing your body.
You'll probably not like your body if you just run, becoming v skinny. Weights plus cardio will enable you to eat (almost) how you want to with say 75% healthy food and 25% 'cheat' and maintain a stable weight.
Up to you but £165 is really nothing, you can have both if you so choose.