You don't need a vent if its within "developed length". That's easy as sin to do yourself, just as said above, cut in a Y, not a T. T's are 90 sharp, and you want the curved down angle of a Y. Keep the brach short, a couple of feet at most, and pitch it to the stack pipe, the main raiser, but only a slight pitch. Terminat the branch with a 90 looking out towards the room/sink and end it with a 2" x1 1/2" male threaded adapter. This is where the jam-nut for the p-trap screws into.
I used to do commercial plumbing for another member on Arf when I was in college and I did the very same thing in my house....except I jack hammered the floor and replaced the old cast iron junk first. It was 50% gunked up at least.
You can buy everything you need at homedepot or lowes, make sure you use primer before you glue.