Sr20 problems

When i first bought my car in the the spring it ran fine and when it started to get cold when i would shift it would bog down for a second then would be fine, but it got worse over a couple days and now when i start it it idles rough and when i hit the gas even just tap it when its sitting there in neutral it will rev down and sputter for a bit and stall but once i get it up to runnin temp i CAN move it its just real hard because it will sputter and want to backfire. (its undrivable just moving it in and out of the garage), i put in a new fuel filter from a 300zx TT and plugs and still the same