Over the years, computer technology has advanced the point that temperature concerns and loud server fans are a thing of the past. Advanced processor technology allow modern systems to not only utilize much less power than they have in the past, but also produce a lot less heat. This means more computing power can be crammed into a small space. There are models ranging from compact 10" deep systems, to 15" deep dual CPU monsters, all the way up to 26" systems with support for full sized expansion cards.
Don't let the small size turn you away, there is plenty of room for both storage and PCI-express expansion. With hard drives growing to sizes of 10TB and beyond, the storage capabilities are nothing to sneeze at. The 1U is also a very good choice for flash storage, capable of up-to 10 hot-swap SSDs in a single system. Most of the models support at least one full-height PCI-e expansion card, with some supporting up to three cards.
There are a few shortcomings, such as limited compatibility with high-end video cards, limited in number of PCI-express cards, as well as the maximum raw storage of 40TB. Thinking about the future use of a system is an important consideration. Will additional storage be needed in the future? Will additional expansion cards be needed? Answering these questions will help you decide if 1U form factor is right for your project.