HD that fit 2009 Mac Mini Model A1283 in need 7200rpm

In theory, yes; any 2.5" SATA drive will work, whether it's a traditional platter hard drive, an SSD, or an SSHD hybrid.

In practice, there may be some limitations. The A1283 generation Mac minis have a 3Gbps SATA II hard drive bus, so faster 6Gbps SATA III drives (the most common ones today) won't be dramatically faster. If the pipe is only big enough to carry 3Gbps, you can't run 6Gbps through the pipes just because you've got a pump pushing out water twice as fast.

In many SATA II systems (particularly laptops), 6Gbps SATA III drives have been observed to behave erratically. The SATA III interface on the drives is supposed to be backwards-compatible with slower SATA II busses, but that downscaling often doesn't work properly, which may put your data at risk.

3Gbps SATA II drives are still available, but you sometimes have to hunt for them. OtherWorld Computing sells 3Gbs SSDs under their own brand. Many older SSDs from Intel, Micron, Crucial, Samsung etc. were also SATA II, if you're willing to buy used drives. Seagate Momentus 7200 RPM platter drives are mostly SATA II; I've used those drives successfully in a number of different 2008-2009 computers.

Most hybrid drives are 5400 RPM, rather than 7200; the drive manufacturers have chosen to use NAND cache flash storage for speed, and decrease the speed of the platter drive (probably to reduce power consumption). The one hybrid drive line that I'm sure uses 7200 RPM is the Seagate Momentus XT, available in sizes up to 750GB. I'm using a 500GB Momentus XT as my boot drive in a 2008 Aluminum MacBook right now; I didn't notice any particular speed boost after swapping out the previous non-hybrid 7200 RPM Momentus drive. More modern hybrid drives use much larger NAND caches than the Momentus XT, but then you get back to the SATA III drive vs. SATA II bus issue again.

The fastest option is a SATA II SSD drive.

SSDs will definitely work.

The 7 and 9 mm thickness drives will fit - the 7mm will likely need a spacer - some drives include them. The guides here on iFixit work very well for the 2009 model.