"to [verb] ______"; i.e. "to play soccer" - please advise

Hi,

I'm trying to prepare a lesson with the following type of questions

"To play soccer is fun"
"It's fun to play soccer"

Notice each sentence contains "to play soccer". Other similarly structured sentences may have "to read books", "to speak English", "to listen to music" .. and so on

I'm trying to find a page that explains the basics of this type of phrase "to [verb] _____" and it's role in the sentences - is it the object, direct influence of the object, etc. Also, further different usages of this phrase used in the following sentences

I want to play soccer
I have a lot of time to play soccer
I'll do my best to play soccer

These three sentences make use of the same "to [verb] ___" but apparently are three difference usages. I want to find a page, or if some kind soul could offer an explanation, that I can learn more. For the three sentences above I want to know the difference and create many sentences, then allow my students to arrange each in groups - that kind of thing. I have tried to search myself but don't really know the name given to this grammar rule if one exists.

Anyway if someone could point me in the right direction or give me some tips it would be very much appreciated.

Cheers
Bizt