building off of what renovator said, if you have load bearing walls on the first floor, you need to align structure below them in the basement. This can be beams or walls. Frame walls will be your cheapest option in most cases. However if you do not want a wall there, then price is not always the driving factor. However if you are a single story plus a basement, you shouldn't have too many first floor interior bearing walls. If you use steel or LVL beams, they must be sized to carry the first floor load as well as the loads placed on the first floor (2nd floor and possibly roof loads). As you can guess, this can make wood beams, even built up, quite deep. Steel might be your best bet here if you have longer spans between columns in your basement to keep head room heights at ideal levels. I tend to disagree with the claim in wood costing more then steel. Steel will cost more then wood in most cases. The post can be hidden inside walls (why would you do this? save the money and make the wall bearing! unless of course you have a very high point load) or they can be boxed out and made decorative. I joists should actually be cheaper then a floor truss, but typically cost a little more then solid 2x8-12 framing. However IMO, I joists are far superior. They can be had in very long spans so they can lay a continuous 30'+ joist across your load bearing beams/walls and allow for straighter and faster construction. Also, depending on the depth of them and the spacing, they can easily clear span 20'+. Plus they are a "greener" product. Trusses will cost more, but the benefit you have there is the web openings to allow easy smaller duct runs and electrical access.

I would not go bashing the wall in with anything - you might hit wiring and pull it out from a box, etc. Instead, make as shallow a hole as possible with a regular hammer or cut out a square with a utility knife set to barely cut through the drywall (don't use a drywall saw - you may cut into wiring!). After you open hole big enough to grab on to, you can then pull off pieces of drywall by hand. A way to get bigger pieces is to score the drywall at the edge of a stud all the way down and you can break off large portions once you cut at the edge of the other stud, but that takes time. Usually just tear it off by hand or with help of pry bars, making sure to not damage wiring and plumbing underneath. At any rate, where a dust mask!

Live_wire_oak, I certainly wouldn’t dispute that most contractors would not use double 2x4’s for a header despite what the code allows (and therefore what is safe). I suspect that you and I know there are many things a contractor does when framing a house that has more to do with just meeting code. It’s much easier to tell your employees to frame every door and window with 2x12s to be safe and not have to do code checks for every opening. I will say though, the better framers in the small minority will take the time to understand what the actual header requirement is so as not to overbuild and create unnecessary thermal bridging.

@ Jeff - I'm glad you have decided to move forward with a professional. If this were a simple gut and reno that had everything IN TACT, it would be worth a DIY job. But your situation is beyond most people's skill level. And that INCLUDES some idiots with hammers that call themselves 'professionals'. Please vet all the people who apply for the job. A homeowner becomes the General Contractor (and all the legal weight that carries) when s/he hires subcontractors (like plumbers, carpenters, tile setters, etc). It is a rare talent that can handle framing (including jacking up as supports), furring out the walls to get them square, flat and plumb as well as a water proofing expert and a tile setter. Please be aware you want to work with a company or group of professionals who SPECIALIZE in bathrooms. They are going to be more expensive, but they *should have all the bases covered.