installing a support beam
You'll probably want to consult with a structural engineer to be safe. FYI, I wanted to remove approximately 9ft. of bearing wall on my first floor. Fortunately, I have an SE friend who ran the numbers and came up with a 1.9E LVL of 1-3/4" x 11-7/8." This too was a first floor application wherein this beam is carrying the 2nd floor joists, wall and ceiling. Keep in mind that you also need to consider what is below the area where the beam is to be placed. Remember that you are taking a load that is currently distributed over the length of the wall and changing it to a point load. In my case, I had to sister 2 existing floor joists and reinforce an existing timer beam below one of the new bearing points. At the other end, I had to build a shallow footing (in Illinois my basement floor is already below the frost line) in the basement and add a new post. All this additional work was in addition to the work of actually installing the beam but was required due to the manner in which the load was being re-distributed. Of course, my home is post/beam construction and was built in 1911. According to my SE pal, the house "does not work" by today's standards but alas, the structural systems in zillions of old homes are identical to mine.
Also, don't forget that you'll need to shore the ceiling prior to removing the wall. In my instance, the overhead joists are full span so I only needed to shore one side. If your joists are spliced over the wall that you are removing, you'll need to shore both sides. My SE friend gave me a good piece of advice to follow, a sort of test to know that the shoring is effective. Go to the center of the span to be removed and cut one of the bearing wall studs laterally with a demo saw. If the saw blade does not bind and the two pieces of stud are not bound at the cut surface, then the shoring is good and you can proceed with the demolition.
Also, if the ceiling framing is not already blocked over the wall to be removed, it's good practice to add some before you demo. Remember that you are disturbing the structure.
I know that you were probably hoping that someone would simply recommend a beam size and off you'd go. Honestly though, and I may be somewhat cautious, but this is one instance where you should probably seek out some real, professional input. An undersized beam may not present an immediate problem but over time, it will begin to sag leading to a whole host of problems like cracked walls, binding doors/windows, leaking plumbing, etc. And the cost to correct structural defects can be immense.
Finally, I'll leave you with a little story that my high school architectural drawing teacher once shared with me. He had this neighbor who hired a contractor to finish his basement. His friend's wife bought the furniture and found that the couch that she had selected was about 2 feet wider than the space between two adjacent pipe posts. So, the homeowner loosened the pipe at the beam connection and using a 5lb. hammer, slid it laterally the required 2 feet. What he didn't know/realize is that in doing so, he moved it off of the pier that was beneath the floor. 2 days later, he received a hysterical call from his wife saying that she couldn't open either of the 1st floor entry doors! They had to have someone come in and jack the house back to level which took a number of days to do. Following that, they had to have several trades come in to fix everything that had been damaged. Beaucoup dollars.
Anyway, good luck.
The very existence of flamethrowers proves that some time, somewhere, someone said to themselves,"You know, I want to set those people over there on fire, but I'm just not close enough to get the job done." - George Carlin