I own a M&P sport and want to know will this trigger fit into the lower receiver Trident Trigger 4 lb Tactical Trigger

Yes it will, for that budget I suggest you look at the ALG Defense ACT too, great trigger for the money.

ALG Defense Combat Trigger - ACT - 05-199 - Primary Arms

Will I don't have a budget set, I was just looking around and came across that trigger and it said it needed to have a small pin .154 configuration, but the lower the price the more likely the wife is to okay it lol.