Welcome to the forum.
What you need to do first is get to the Philippines then you can start planning your future together if that is what you still want once you have met.
You can sponsor her for a visitor visa, though there is no guarantees that it will be granted. Though recently it does seem that they have been more willing to grant them.
Whether you got for a fiancee visa or a spouse visa depends where you want to get married - UK or the Philippines? Spouse visas are slightly cheaper and easier to get than fiancee visas, but really it comes down to what you want to do.
Flights to the Philippines seem to work out upwards from maybe £400 depending who you fly with and when you fly. When visiting Manila I tend to stay in Makati at one of the 5* hotels near the main shopping area there (think I paid ~£75/night earlier this year) which is very safe area to stay. You can get safe hotels for less if you don't want to spend that much. If you are going to stay there for a couple of weeks you may want to take a trip away from Manila as to be honest it's not the nicest place to stay.
