The best method, is to insulate the OUTSIDE of your foundation. That's the process I'm in. That option mitigates many of the humidity/moisture issues, you most likely won't need a de-humidifier in the basement anymore, it puts the foundation inside the heating envelope so it buffers against heat/cold spikes, no mold/mildew issues, very little water issues, but you have to worry about termites in certain areas. It takes me 40 hours to insulate 12 feet of the exterior my foundation. Tell me if you plan on insulating the outside and I'll go into the steps, but if you're like me and doing it with a shovel, it's hell... though I definetely feel the effect of the exercise on my energy and concentration.
To insulate the inside, don't put fiberglass directly against the foundation wall. You risk having the humid basement air work it's way out in winter and the moisture will condense on your basement wall and fiberglass insulation causing mold/mildew issues, or in summer water whicking through the foundation will condense on it causing the same. Use a layer of XPS, at least 1" thick if not 2", that's extruded polystyrene directly against the foundation wall. It's a type of readily available foam board, that never degrades by water or in wet environments, water itself can't penetrate it, mold doesn't like it, but allows water vapor to pass in/out and it will move the condensation point inside the middle of it, or behind it instead where it won't matter. Use a wire brush and clean the foundation walls. Then use a big caulking gun and tubes of PL and adhere the XPS to the foundation. I spread the PL in a big pattern around the edges of each piece of insulation, you want to prevent air leaks, and then put dotted lines in the middle. Push it and hold it tight to the foundation wall, you want to make sure it's tight. Leave 1/4" space between each sheet (it normally comes in 4x8). Once it dries and holding, use expanding foam (polyurethane not latex) between each seam and follow the directions on how much to fill each gap, after it dries cut off excess. The foam cans are usually one time use, so if you want to take a break stop after you run out of a can. That should ensure an air tight and insulated wall. Caulk the tops & bottom of each sheet to stop air flow. Now, you should have no moisture problems (unless it comes up through the floor). You can do any number of things at this point, but it must be covered with drywall. You can now place 2x4 stud wall over it, fill the space between with fiberglass batts, and cover that with drywall and you've now got some serious insulation, or if you're happy with the amount of XPS insulation you added you can get furring strips placed every 16" and cover that with drywall. However, the studs or furring placed over the XPS must be attached to the foundation with mechanical means, it's against building code to only have it attached by adhesive. In a fire or high heat situation, the adhesive can become soft and fail, and everything come tumbling down exposing the highly flammable parts if never mechanically fastened. As a tip, you'll probably be using tapcons to do it. If you've never used them, they only go in about 1" and then they lock up, trying to get them in over an inch you'll normally snap them instead. It's better to pick a tapcon that will only go in 3/4" than attempt to get one in over 1". If you have water issues on the floor, keep the drywall 1/2" off so it doesn't wick it up, or use cement board on the lower portions. Also, use pressure treated wood on the bottom for the stud walls if going that route.
As for the sill plates/rim joist area, caulk any seams in the area to prevent air leaks and the best method is with tubes of silicone that come in tooth paste tubes. It's nearly impossible to get a caulking gun in there, and the spray foam has to be applied upside down making it difficult as well, but the tubes of caulk are easy. Caulk the top where your rim joist meets the floor, caulk the bottom where your rim joist and sill plate meet, and if you can caulk where your sill plate meets the foundation. Then, once again use XPS foam. Many people use fiberglass batts, but it doesn't stop air movement, they normally settle slightly and pull away from the rim joist and leave gaps making them nearly useless. I haven't seen a house with the rim joist/sill plate area insulated with fiberglass only that hadn't become almost useless in a year. With the XPS, make it as tight up/down as you can and leave a small gap on each side. After putting it in place, caulk the top & bottom of them, and use a bead of the spray foam on the sides. The stuff is VERY easy to cut on a table saw, but wear eye protection and a breathing mask. If you run across any pipes in that area, it's very important you don't insulate over them. I normally take the couple pieces of XPS for the bay (I put 4" thickness in), cut in half to get behind the pipe, and then I caulk it normally along with the seam in the middle afterward. Leave the pipes exposed to the basement air.
The floor, the proper method is to cover it with 6 mil plastic, with XPS once again on top of that, with furring strips spaced every 16", and 1/2" plywood on top. That's a lot of space you loose off the height of your basement, and honestly unless you have moisture issues in the floor I don't see it as a priority.
Oh, by the way there's a federal tax credit of 10% on insulating the envelope, this is part of it and up to $500. Also, if in a financial crunch, insulating only the top half of your basement is about 70% of your heat loss from it. However, it's usually financially not much more to just do the whole route. Don't bother insulating the floor above if you did the walls.
