I don't think your budget will get you a house in Zug/Baar, it's an expensive area due to the low taxes, and supply can't cope with demand, so you'd be looking at apartments. If you want a house, throw your net a little wider (I live just over the border in Kt Zurich), and the choice of property on offer for that budget is much greater, and the cheaper rents more than covers any addtional tax my wife pays.

She can get to Zug banhof in 12 minutes by train, and there is way less traffic so if we drive door to door (Landis & Gyr strasse) is about 20 minutes.

www.homegate.ch or www.immoscout.ch will be your best bets.

The Chamerstrasse apt is cheap for a reason, it's right on the main rail line for S and inter regional trains, and on one of the busiest roads in Zug. I have firends who lived in the next building and they lasted 6 months before the noise got too much.

For the permit, were accepted for our apartment before my wife's permit came through, we simply had to provide a copy of her employment contract, and a copy of the permit when it came through, this was the same for opening the bank accounts.