Don't even think about finishing the basement until you have the efflorescent issue nailed. With that much moisture coming through the wall any finish-wall materials you put over it would be under a serious vapor-pressure and mold threat. Even fairly vapor permeable paint is likely to bubble and peel, and impermeable paint would fail even more quickly.
This one looks serious enough that I'd even consider digging up the foundation and applying a waterproofer on the exterior. :-(
When you think you DO have the efflorescence issue licked, anywhere in MA it's worth putting up at least R10 or even R20 of insulation between the concrete and the conditioned interior, even on sections where it's completely (or mostly) below grade. The cheapest way to get there without creating moisture problems is to put either 2" of either unfaced EPS (bead-board, like a cheap cooler), or 1.5-2" XPS sheathing against the concrete, and trapping it there with an interior studwall for running your power, etc., then use UNFACED R11-R13 batts in the stud bays. The whole-wall R of the different stackups break down as roughly this:
2" of EPS + studwall___________R18
1.5" XPS + studwall___________R17
2" XPS + studwall____________ R20
Given how much moisture is going through the wall, it's probably better to use EPS rather than XPS, since XPS is more vapor retardent, and the moisture content of the wall could rise to the point where it puts the foundation sill at risk. Don't use foil-faced iso either, just EPS (up to 4" absolute max) or XPS (up to 2").
Use 2" of closed cell spray foam to insulate & seal the band joist& foundation sell to the top of your wall foam & studwall. (Band joists & foundation sills typically add up to more air leakage than all of the windows in the house combined!)
This is a condensation proofed vapor flow-through stackup- you should NOT UNDER ANY CIRCUMSTANCES use any interior vapor retarders (like kraft paperfacers) or vapor barriers (like poly sheeting, foil wall paper, oil paints, vinyl wallpaper) on the interior or you can screw up the foundation sill with high moisture. The R value of foam is sufficient to limit the condensing hours in a year on the above grade sections, and below grade it will never condense. Use a sill gasket under the bottom plate of the studwall to avoid wicking ground moisture from the slab. If you are putting in a finish floor other than tile (wood or particularly carpet), put down at least 1/2" of XPS between a wooden subfloor and the slab, and continue the XPS under the bottom plate of the studwall all the way to the wall-foam. That prevents moisture from wicking up to rot out the bottom of the flooring materials, and sufficient R to prevent summertime moisture & mold from growing in carpeting.(It'll be more comfortable too.) There's a long term financial argument for going as high as R8 on the floor from a heat-loss & fuel use point of view, but you may not have the head room for 2" of EPS or 1.5" of XPS + subfloor+ finish floor, which can also complicate basement stairs and doors, etc. With only half-inch foam an half-inch OSB as a sub floor you lose less than 2".