It depends on what you want to do and/or what group you want to be a part of.
There are a few large organizations made up of smaller groups and a lot small groups with no affiliation.
Most groups I know will go to an event and set up a camp to portray life in their time periods. Any number of basic everyday activities may be demonstrated in camp. If there are enough fighters they may put on a demonstration of combat, whether scripted or competitive. Most groups have basic armor standards for this. Some allow archers to participate in battles by using arrows with the points removed and replaced with specially padded heads.
If you have a whole family and they want to come, by all means bring them, but it is not required. But dressing the part is essential. Hanging around the camp or fighting in jeans and t-shirt ruins the whole thing for everyone involved.