You can finish this space a number of ways. All the choices are based upon your projected use of the space. And your budget. Even the DIY approach will cost money. Gone are the days of $1.50 sheetrock and 89 cent studs. That would be the early '80's(1980's) for the youngsters out there.
How much is sheetrock up in Canada?
Why don't you provide some details and we can project how likely this will get done to your satisfaction.
Ron

Thanks Ron
The space is 420 sq ft. One room would be a family room for tv etc. and the other a bedroom for company. Sheetrock in Canada is about 12 dollars a piece. I really would like to make sure it is as cosy as possible. We would most likely have a pellet stove for heat. Pretty basic really. Is the powdery mildew a huge problem. I notice it in someone else's mostly finished basement.

You need to control the moisture level in the basement. Weather permitting I would check to see that the grading on the outside slopes away from the house. That there are no low spots that fill with water when it rains. That the leaders coming off the house are at least 3 ' long to get the water away from the foundation. Make sure that the gutters aren't clogged and overflow down the side of the house.
I'd install a dehumidifying system so excess moisture can be eliminated. Here on LI,NY the dehumidifier runs from May through October. I have it run into the sink so I don't have to empty it all the time. It can easily take a gallon of water out of the air in a day.
I would clean the concrete walls with a solution of chlorine and water, let it dry and paint it with a product made for concrete walls. I used a product made by Thoroseal. Sort of a thick paint with cement integrated into it. There are plenty of choices.
I'm not a fan of wood up against concrete walls. When I do basement renovations I leave at least an 1/1/2" gap around the perimeter for air flow. I use metal studs, fiberglass batt insulation(unfaced) and a vapor barrier. Metal studs have gotten pretty pricey but they are much faster to use and already have the holes in it to run wiring.
Bedrooms in basements here require an egress window installed. I don't know if this will be a DIY job with no permits or you need to file plans. Expect to pay between $4000-5500. to have one installed.
Ron

Thank you Ron for all the advice. I will start taking the walls down tonight. I love demo. lol

Before you go and vapour barrier that basement, take a look at what the leading building moisture expert has to say about that method. Particularly, look at the pictures on page 20 on the PDF version.

And whatever you do, avoid steel studs. Unless the space is sealed from water vapour, steel is the perfect material for water condensation to feed the mould that will develop there.

Mechanical dehumidfication and steps to keep liquid water from entering the structure is excellent advice that should always be followed.

In the past, I regret having followed the Code and used the double vapour barriers it requires. I've seen the light and now use XPS insulation, e.g. Styrofoam-SM, or sprayed foam, no vapour barrier and drywall. Good luck with your project!

BTW, I am a licenced TARION builder in Toronto.

Thanks Worthy
What would you suggest I do with those 2 by 2's against the cement. I took off all the old paneling today and found the white mildew on the bottom of the walls only and every thing looked dry otherwise. I felt the strips of paper that he put behind the studs and they were all dry to the touch as far as I could tell. I am going to read what you sent me but will I get it? lol thanks again

The white deposits sound like efflorescence. These are salts dissolved off the masonry by the flow of water, water vapour or hydrostatic pressure. If the wall doesn't smell musty, it's likely these are old deposits and may not mean much.

Unless there is water coming through the wall, I wouldn't use the sealing products. In fact, they could cause a problem trapping water vapour in the wall at the top where it is above grade.

It's hard to say about the 2x2s. If they come out easily, I'd remove them. But if they leave holes, be sure to patch them with hydraulic cement or other suitable product. (If the wall is unit masonry, the nails used to put the 2x2s' in might have rusted and formed a block to water.)

I put stud walls on top of a 1/2"-1" strip of Styrofoam-SM. The Code only requires poly, but if there's flooding for any reason you don't want the wood to sit in water. Same thing with the drywall; keep it a good inch off the floor.

As pointed out above, be sure to avoid all exterior sources of water entry. And use mechanical dehumidification.

And no batts unless you've got XPS tight to the wall first.

Here is a link that might be useful: Healthy Affordable Housing