Gate checking works really weel. Ask about it when you first check in for you flight. They might tell you to check with the gate agent when you get to the gate, but sometimes they will give you a gate check tag at the check in counter. If you have a connecting flight and want the wheelchair deliverd to the gate there, make sure they have marked the tag for it to be delivered there.
before you leaave the wheelchair at the gate, fold it (if it folds), make sure all seatbelts or other straps are fastened so they don't catch on anything. When my DD had a wheelchair seat that was just attached with velcro, we used to remove it and bring it on the plane. if you do that, most of the pieces you take off whill fit in the overhead bins.
If the wheelchair fold up fairly small, you might be able to fit it in the closet on the plane. Whether you can do this or not depends on the size of the wheelchair and the size of the closet. It can be a lot of hassle. They have to let you try it in the closet if you want, but the flight attendants are often not real helpful because the closet is usually used for the first class passengers' coats and hanging bags. They are not too happy to have "their" closet filled with a wheelchair.
The airlines do have Special Needs Departments (they don't advertize it too much). They can help you with seat assignements and answer questions about gate checking/closet storage.