will any mobo fit?

You're not limited to "brands", but you must use the same form factor. Atx and micro atx are the most common. If in doubt, a micro atx will fit in an atx case.
Though replacing a motherboard may mean you have to buy a new copy of windows.

 

Hi,
I am pretty sure an ATX mobo will have a 20 pin power connector.
The Micro AT will not. I would do a search on ATX & AT specifications.
Your power supply may come into play too.

Good Luck.

 

Take the measurements of your mobo, and compare that with what you want to buy.
New(er) mobos quite often require a new CPU and different memory from what you have got. If you have integrated graphics, you will also need either (rock-bottom) integrated again or a new (low-class) PCI or (middle-class to very good) AGP or (top of the line) PCI-Express card.
A more powerful power-supply may also be necessary.

From your description I gather you have a veritable piece of eMachine junk.
You'll be better off buying a new barebones system, rather than waste your money trying to soup up a piece of crap.

For swapping a mobo, you do NOT need a new copy of Windows. You WILL have to re-install from scratch though, and in case of XP, you will almost certainly have to re-activate it (only one phone-call away).