1080i & 1080p question

[jayson decambra]

good day everyone. im a new user and kinda new to blu-ray. i have a PS3 as my blu-ray player and i have a 32inc LCD HDTV. my tv is an olevia (i know not the best, im saving for my sony) and i know it does 1080i. i dont think it does 1080p. im pretty sure i have all the settings correctly cause the games and the movies look pretty dam good but my question is this.
last night i bought "live free or die hard" and on the cover it said "1080p" HD, ect, ect and all this other stuff but i noticed it didnt say 1080i at all. how does this all work, i mean if i buy a blu ray and it says 1080p does that mean it wont play to its best on a 1080i tv or vs versa?

i know thats prolly a rediculous question but im new to the whole blu ray thing. and if possible someone could maybe take the time to tell me what my tv settings and ps3 settings should be that would be great.

thank you in advance.