What the guys have said is true, you will need new footings installed under the posts ..as you said also.
The question I would ask myself ...and an engineer...is why was there a wall there to begin with?
Posts are much cheaper to install. But I think they installed a wall to get rid of some of the deflection of the 2x8 beams and joists. The span is more than 12 feet on the joists, right? And the floor has a little bounce to it also? When you remove the wall ,you will have more bounce because the weight is transferred to only 3 points, no longer continuous. If you can live with that, you need at the minimum 12 inch deep by 2 foot square footings. Now this is just an estimate because we do not know what you are holding up and where the point loads are on the beam. We also do not know where the posts need to go . They need to be at the joints of the beam, however if there are any posts in the upstairs walls...you need to transfer the weight directly below these posts from above. So you may need more than 3 posts.
My opinion is to get a professional in to give it a look. They can tell you exactly what you need, and keep you out of harms way.