When my children were younger, we used gates to close off areas of the house to keep the children safe. As they grew, we increased the size of the area we let them play in, but didn't let them have full run of the house until they could understand and follow specific directions, usually around 3 years old.
We first had our den gated off and kept my daughter in there most of the day before she could walk. Someone was always in there with her, or just beyond the gate where she could be seen at all times. Then when she started to walk, we took down the gates around the den and included the dining area which was right next to the den. When she started talking and could follow basic instructions, we moved the gates to include the kitchen area, but still kept the stairs and the formal living area off limits. Then, as I said, when she was able to understand and follow instructions consistently, we eventually took all the gates down and let her roam free.
Of course, during each stage, she had plenty of age appropriate toys, games, books, videos, etc., to play with and learn from. In fact, the den area of the house became so overrun with toys that we just made that the permanent play room and started doing our tv watching and socializing in the formal living area so that we could all be downstairs rather than making the kids always play upstairs in their bedrooms and out of the way.
I think rotating toys every week and spending as much time as you can with your children, even in a confined area is fine. Think about children in day care. They often only have one room to roam through all day and that seems to be socially and physiologically acceptable. They do have set activities and also get "outside" time a couple times a day so I do think that's important, but I wouldn't feel guilty about giving your children a safe place to play as long as you're spending a significant amount of time engaging your children in fun and/or educational ways and you can expand the area as they get bigger.