Yes, the case determines which motherboard type you can use, mainly by its form factor, which dictates the motherboard size and mounting holes available. The most common form factors for normal-sized computers are ATX and microATX.
Standard ATX is the most common and is used in mid-sized and bigger cases. ATX motherboards are full sized and can only be used on ATX cases. microATX (also called mATX or µATX) has a smaller, more "square-shaped" motherboard, which allows it to be used in equally smaller mATX cases as well as standard ATX cases (the mounting holes can accommodate both).
When you buy your parts online, the form factor is almost usually mentioned in the product description for both the case and motherboard, ex:
BIOSTAR P4M900M4 478 VIA P4M900 Micro ATX Intel Motherboard
Antec Sonata III 500 Black 0.8mm cold rolled steel ATX Mid Tower Computer Case 500W Power Supply - Retail
You select a mobo (motherboard).
The mobo manufacturer and sometimes, the store, states the form factor at their website.
For additional information about form factors, including dimensions and images,
Once you have selected your mobo and know its' form factor,
You can decide on the computer case/chassis.
With that said,
Pre-built systems from tier-one manufacturers,
eg. Compaq/HP, Dell, IBM...
May use proprietory designs.
And If you want a recommendation I'd say stick to motherboards and cases that are ATX and not Micro ATX.
Nothing wrong with the performance of Micro ATX motherboards, but upgrading certain components can be more difficult, especially if you've got a small computer case (mini tower) that only supports Micro ATX motherboards.
Would I get bashed on for asking lots of questions here, I would do research, but if all else fails, is this one of those friendly forums, or one of the ones where the members don't like helping? (no disrespect)