If you're bidding a project, all bidders should be provided with a set of plans and uniform specifications. What to use as a vapor retarder and where to place it in a wall assembly should be shown and specified in the plans not left to the builder's discretion. If your design professional is a little lacking in the building science department, here's a link to kick off your own search:

https://www.energy.gov/sites/prod/files/2014/01/f6/1_1a_ba_innov_basementinsulationsystems_011713.pdf

Expanding on the above, see Building Science Corp. on basements.

Still idiots out there recommending fibre glass alone for basement insulation?? On their own YouTube channels, I expect. (And behind the desk at the Big Boxes.)

Yummy for mould! Fibre glass behind vapour barrier.

Diapers for your basement.

Dehumidification is a must in most climates in the summer. A single portable unit in an open area is all most basements need.

IMO you need to adress the water issue from the outside first .

A happy middle ground is applying XPS insulation board directly to the foundation walls, which will act as a vapor barrier and insulation. Then install a wood framed wall and drywall over that. 2" of foam is usually adequate; 3" is better and meets code in many areas of country.

Pick your poison:

https://www.owenscorning.com/en-us/insulation/residential/products/basements?customer=residential

Fiberglass insulation can be used--just not in contact with basement walls. If you look at the DOE link in my post above, they show fiberglass batts used in conjunction with XPS that is applied directly to basement walls. I'd prefer foam in lieu of the fiberglass, but that's a personal preference. Polyethylene sheeting shouldn't be used as it will limit drying to the interior.

All that said, the bidders should be provided with a set of plans and specifications that leaves nothing to question. You won't get the same result from some handwaving and verbal descriptions. Indeed you'll be left to sort through a bunch of different approaches and pricing and it may make your head hurt.

they show fiberglass batts used in conjunction with XPS that is applied directly to basement walls

I've done that. But I note that Martin Holloday, formerly of Green Building Advisor, advises against any moisture sensitive material on foundation walls; he also warns against using mineral wool batts against the walls. FWIW, the tightest basement I built used 2" of closed cell spray polyethylene foam (ccspf) on the walls.

Patricia is right, the real work to waterproof a basement starts on the outside. You’ll need to excavate along the foundation and add a membrane, drain, crushed stones etc. it’s a big job but otherwise the concrete is always going to wick up moisture and it will always come through.