Most rack mount servers come with rails. There are two types of racks: square hole, and round hole. If you got an APC rack, it's probably a square hole rack. Depending on the manufacturer of the rack mount server, you can either mount the server rails "toollessly" or with screws. The toolless method is preferable as it is easier and faster. Any server you buy from a manufacturer like Dell will have rack mounting instructions.
PDU=Power Distribution Unit. You can think of it as a glorified power strip. These PDUs come in three major types: basic, metered, and switched. The basic PDU is the closest to a power strip. One end plugs into a receptacle for the input and the strip offers many receptacles for you to plug in your gear. Next up is the meterd PDU. It's the same as the basic PDU but with an extra feature that tells you the total amount of power drawn, typically reported in Amps. You want the power draw in Amps to be less than or equal to 80% of the rating of the branch circuit. So, if you plug your PDU into a 20 Amp circut, keep the Amp number at 16 or lower. This is for safety and is required by law. The final type of PDU is a switched PDU. This has the features of the basic and metered PDU along with another trick. You can connect to the PDU using a telnet or web client and remotely cycle the power to an individual outlet or receptacle. This is useful for remote reboot or to install a new image on your rack mount server remotely.
The best solution is what's called a 1U Monitor/Keboard setup. It slides into the rack like the rackmount server above. It is typically mounted on rails as described above and takes up 1U or 1.75" of rack space. When you slide it out, the monitor levers upward into a viewing position. When you're done, you simply slide it back into the rack and it collapses into a 1U space again.
This is an open question you'll need to answer yourself based on your needs. There are advantages and disadvantages to each name brand and so-called whitebox machines. For your first server, it will probably be easier for you to get going with a name brand just because these tend to be more standard and easier to rack.
Same answer as above. Tough to say without knowing more. It's not too hard to buy a rack mount server from Dell or any of the other main manufacturers for that matter. A local vendor can be a good resource so if you like them, ask for their opinion as well about chosing an appropriate server vendor.
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