Kari,
We are currently finishing up two rooms in our basement that are used for storage and a workshop. Today we finished the floors (I'm 8 1/2 mos preganant right now too!) My husband and I are a couple of do-it-yourselfers and have completed all kinds of home improvement projects. We think it's fun (yes we're a little odd)
If you don't want to drywall the walls, you will have to paint or use some form of plaster/cement. One thing you need to check first is for moisture seeping through the walls. I'm not talking about obvious leeks, but the slow wicking of moisture over time. Old houses tend to do this because of the materials that were used during construction. If you have clay brick walls, these will definitely wick mositure. You can test for this easily by taping some paper to the wall and covering it with a plastic bag to prevent moisture from the air getting to the paper. After a few days, peel off the plastic and check for dampness of the paper. If the walls are damp, you will have to use some form of waterproofing prior to applying anything to the wall, either drywall or paint/plaster. Dry-lock works well. Once you apply the dry-lock, you can paint any color over the top of it.
Just be sure to prep the surface appropriately, the manufacturer will tell you what you need to do. This step is time consuming but it is CRUCIAL. If you don't prep the surface right, even the dry-lock won't work well , and then you will have problems with whatever you put on top of that. This may ionvolve acid etching the concrete and or cleaning with a strong detergent. Home Depot caries all of this. The other drastic water-proofing is to do it from the outside, but I would only use this if you have a SERIOUS moisture problem.
If you aren't going to drywall and want to hang things on the wall, consider hanging things from long cables from the celing joists. Just be sure that if you are putting holes in the wall, they are above grade, or you somehow epoxy around them to keep the moisture from leaking in. You will need a hammer drill to put holes into the concrete. You can rent this from Home Depot as well.
As for the ceiling, you can drywall it or they make drop ceilings that are actually flush mounted to the joists, so it's not really drop. These are actually quite nice looking as opposed to the old drop ceilings that we are used to seeing. You can find them in Home Depot or Lowes. I would not be a fan of fabric or plastic sheeting since these will begin to sag or rip over time, and then it just won't look very nice or professional. We had plastic up over insulation in the two areas we have now drywalled. They began to sag and the drywall looks MUCH nicer. Whatever you do, be sure that you will have easy access to water and gas shut-offs. In the two rooms in the basement we are finishing, there are no shut offs, so we could put up drywall. For the rest of the basement (when we get to it), we will use the flush-mount drop ceiling tiles so that we can have access to shut-offs.
If you decide that this is too much work for you and want to use a contractor, make sure they keep in mind everyhting I just told you about moisture. Not all contractors do a good job and then you will have wasted a lot of your money on something that will need to be done again.
Let me know how it goes. Good luck!
N.