Welcome to the forum.
Packers tickets have been sold out on a season ticket basis since 1960. You can however, purchase tickets from season ticket holders, through sites like titletowntickets.com (I use titletowntickets because it is the cheapest), and packerfantours.com , among others.
Tickets are mailed to season ticket holders on August 1st. So if you purchase tickets from any of these sites, you will not receive them until after August 1st.
If you need to stay at a hotel, I would suggest the Bay Motel and Restaurant, as it is one of the cheapest, (its nice too!) and it is only 1 mile from Lambeau.
There is a 2 night minimum at pretty much all the hotels in Green Bay when the Packers are in town. The Bay Motel, as I mentioned before, is one of the cheapest at $100 a night for the first two nights, and I believe 35 for any night after that.
If you are looking for a cheaper option, and don't mind a short drive, there are hotels in Appleton as well, that do not have the two night minimum inflated rate.
If you have any more questions feel free to ask.