LGA 775 vs LGA 1155
I can't find any proper answer on this. Is LGA 1155 better in performance than LGA 775? How much? If I buy LGA 775 for Quad Core, Will it support i3 and i5 CPU? Or only Simple Quad Core CPU?
1155 is better, its also quite a few years newer. if you buy a 775, it will only do 775 supported processors (core 2 duo, core 2 quad, etc). if you want to use the more recent (second and third genereation) i3/i5/i7 you will need an 1155, if for some reason you want a first generation i3/i5/i7, you will need an 1156 motherboard
LGA775 is a dead end, it was replaced by the newer sockets LGA1156 and then LGA1155. You will not be able to use an i3 / i5 / i7 CPU on the older LGA775 motherboards
In terms of performance the newer sockets always provide a performance jump, how big depends on which CPU you use and for what purpose
This will give you an idea of performance difference. If looking to upgrade, I would just wait till the new Intel cpu's come out next month. It will be a brand new socket and will have a better upgrade path since the current gen i3-i7 boards will be a dead end.