Georgia-Pacific GP Lam Laminated Veneer Lumber (LVL)
An LVL is 50 times stonger then milled lumber and can run longer spans with less support from below, but your going to have to do some research to figure that out.
You would use the hangers made for LVL's (there wider) to reattach the old floor joist, and reguler ones to attach any sistered joist if there's room for them, sometimes I've used HD L brackets with the larger holes for lag screws when a hanger will not work.
The new beam will never come out the exact width as the old beam and LVL's only come in two widths. I suggest using the 1-3/4 ones, for one thing there lighter, and it's simpler to lift into place with the small gap you have to work with between the old floor joist.
Before any post are sat in place check for any floor sag, now's the perfect time to use the beam once the floor joist are reattached to lift the floors up before putting the coloums in.
Use lolly coloums or soild steel post with 1/2" steel plates welded to the ends with holes drilled in the plates in 4 places for nails or screws.
Anyplace there's going to be a post there has to be a footing. 24" X 24" X 24" deep. You can not just have them sitting on a 4" thick slab!