A good variety of choices are available for indoor cages. Many people start with large bird cages.
All bird cages are not constructed the same. If you choose a bird cage look for the ones constructed with the bars inserted through the framework for strength as a monkey of even moderate size such as a capuchin will soon shake the flimsier varieties apart. The pros of a bird cage is they fit in smaller areas when limited space is available. They have removable trays for ease of cleaning. They make a double cage that offers a larger play area while providing an extra cage if needed or can act as a shift cage if the monkey isn’t handled or someone else needs to care for them. The slider is inserted with the monkey on one side so you can change out bedding toys and clean. The down side is lack of space. So these should only be used for the primary cage if you have no other options.
Flight cages offer more space. They do not have floors so you will have to go in to clean the floor as there are no trays to pull out.
Priefert or Behlen Magnum (if you can find used as the new ones are lighter weight and no longer powder coated) cages are a good choice if you have space and will last many, many years. The smallest available 5 x 5 feet, with a 5 x 10 feet providing a good amount of indoor space for most monkeys. The 10 foot panels enable you to design any size cage you choose and enable easy expansion if you desire more space as your monkey matures or you add other monkeys to your troop. These heavy duty panels are powder coated which gives many years of use. The panels are also of a size that can be moved if you relocate or just want to change the location of your cage. You can purchase extra panels for the top or use horse panels.
Some people turn a bedroom or other extra room into an indoor enclosure. The key consideration when doing this is safety. You will need to cover any windows with some type of bars, heavy wire (horse panel) or heavy duty Plexiglas. Electrical outlets and light switches will also need to be covered with something the monkey cannot reach into and the light fixture set and secured so your monkey cannot reach it. Walls and floors need waterproof materials even if your monkey will be diapered. Most people choose to cover the walls with FRP paneling. Make sure any eyebolts inserted for swings, hammocks, etc. are secured into framework of the ceiling and not sheetrock to prevent an accidental fall which could injure your monkey.
Small monkeys such as squirrel monkeys, marmosets and tamarins require caging with smaller bar spacing or 1-inch wire.