existing beam at the location where the post is to be removed must be continuous without splices to make this work.  Assuming it is one piece, to strengthen the beam, there is no need to provide a U shaped steel on the underside.  Although side members will provide for little additional strength majority of the added stregnth will be from the bottom steel.  I recommend providing just a thick enough bottom plate.

As for thickness of the plate and number of fasteners to connect the new plate to the existing beam, I recommend you consult a local structural engineer.  Solution depends on many factors such as span, end condition, floor loading etc.

I would sugest not to carry out this work whitout calcualtions. Have a structural engineer not only design the beam, but the shoring to do the work To help him out, try to locate the structural drawings of the existing building if you can.

Pull out a construction permit. If in the future there is a problem like strucutre cracks, or wahtever, and the insurer finds unpermitted structural modifications were made, they may deny coverage, and righfully so. It would be for your own safety also.

I agree with both of the other responses.  Hire a local structural engineer to evaluate you exact condition.  The cost of the engineer is worth being able to sleep nights knowing that your bedroom won't be in the basement in the morning.  

All joking aside, depending on many columns you plan on removing you may actually need to replace some of the existing columns and replace or reinforce the footings.  Since you now will be supporting more load on the "end" column, it will probably need to be replaced.  Typically, in my area (NE) basemnents have concrete filled lally (not lolly)columns, usually spaced about 7-8 feet on center, supporting the girder.  Depending on the height of the column (usually about 7 feet), the column capacity is about 10kips.  As soon as you remove one column, you will overload the existing lally.  

The footings beneath the lally columns are usually about 2 feet square (depending on local soil conditions).  Assuming an average bearing capacity of 4,000 psf.  The footing has a capacity of about 16 kips...ASSUMING THE CONTRACTORS ACTUALLY LOCATED THE FOOTINGS AT THE CENTERLINE OF THE COLUMN.  Usually the footings are off a few inches which will reduce the allowable load to the footinmg to somewhere about 12 kips.  Again, once you remove one column, the footing is overloaded.