The larger Key West hotels and resorts have at least a hundred rooms and suites, good beach frontage, good swimming pools and spas, and onsite dining facilities. These include the historic Casa Marina Resort, which is the largest with 300+ rooms and suites. Doubletree, Hyatt, Sheraton, Westin and others are in this category for you.
You will find a few hotels with under one hundred rooms. They provide several but not all of the things you would see at the larger properties. With two such properties, Hyatt is number one in that department.
There are some wonderful Key West hotels with fewer than fifty guest rooms. These are such places as the Marquesa Hotel, the Gardens Hotel, the Sunset Key Guest Cottages and the Santa Maria Suites. You should find one worth a visit.
Key West has most national hotel brand names present and some of them are not as pricey as the luxury brands. You will find Courtyard, Fairfield Inn & Suites, Best Western, Days Inn, Travelodge and others.
You'll find some discount rates at smaller non-franchise hotels and motels that don't carry a national name you know. Not being franchisees, they can set their own standards of service and cleanliness. Probably some of them are suitable. I have not stayed in any don't choose to name any. You could be a winner.
Bed and breakfast facilities are all over Key West. As the name says, your stay includes a daily breakfast, which usually is continental but could be a full one. The number of rooms is smaller than in the hotels and the rooms vary in styles. You might have to share a bathroom with others. An owner or manager will give you personal service.
The Key West Youth Hostel is alone in its category. You'll find the cheapest rates in town. You will receive a bed in a large room and access to a common bathroom and kitchen. If it matters, be advised that no alcoholic beverages are allowed.