Short for Next Unit of Computing, these tiny boxes are desktops built on mobile and sometimes desktop processors. They don't produce much noise or heat, but you wind up paying a premium for that. While they scale out quite nicely, their scale up ability is hampered by the form factor, and will require external storage of some sort. The NUC makes a great candidate for hosting vCenter and a vSAN witness node for 2-node clusters.
AMD also builds "NUC" like form factor systems, but lack Thunderbolt (for now). There are third party vendors that make tiny form factor desktops, but often use Realtek NICs which (again, for now) are not compatible with ESXi. If you buy one of these, be sure to also purchase a compatible USB NIC and load the USB Network Native Driver Fling.
It is worth noting that second hand workstation laptops can often be had at a similar price point. While these sacrifice form factor, they allow for a little more storage, have a display, and also have a built in battery. The same amount of USB/Thunderbolt ports can be had as well.
Referring back to my 2020 Homelab Buyer's Guide, rackmount servers are the go-to for most datacenters. Second hand servers can be found on eBay for a fraction of what they sold for as new, as e-cyclers resell off-lease and retired equipment. While this hits the sweet spot in terms of price, capacity and performance, this is easily the loudest and least space efficient design on the chart. Rack mount servers... well, require a rack to mount them to. You can get away with stacking one on top of another, but you'll be cursing yourself as Murphy's Law takes out a memory module on the bottom server. 2U servers tend to be quieter, and some have better fan controls than others. Unless you have a dedicated room or shed that is properly prepared for such an endeavor, I'd suggest looking at other options.
Although workstations are not servers, they have a lot in common. The Precision T7810 and HP Z840 are both examples that share the same processors with 13G/G10 servers, and have a large number of PCI-E slots to work with. Workstations have less memory capacity, require dedicated graphics (no onboard VGA chipset, critical callout if you buy a barebones setup), and cannot hold as many drives (usually 3x3.5" cabled). For these reasons, they come at a significant discount as they are viewed as prosumer equipment. Noise is practically an afterthought, but this is due to the large form factor supporting larger fans. Proper planning should be taken if more than one is purchased - these are not apartment friendly. Workstations will often check most of the boxes for performance/dollar/noise ratio.
Tower servers are intended for small offices, for those that need the power of a server that can comfortably sit under a desk. Unlike workstations, these have much larger capacities in terms of memory and hard drives. For instance, the PowerEdge T630 can hold up to eighteen 3.5" disks, or 32 2.5" disks. This makes it a great candidate for a diy NAS. Tower servers can often be converted to a rackmount configuration as well, giving them more versatility should you choose to incorporate rackmount servers. Because tower servers have much greater memory and disk density, these command a bit more of a premium than tower workstations. Again, towers are not apartment friendly in terms of space.
Instead of camping eBay, waiting on a shipment (if it ever comes), planning where you're going to put the things when they arrive, cursing out network equipment, finding out the server requires 240V, etc, etc... why not just spin up a container in the cloud? The big three (GCP, AWS, Azure) all have a free tier/trial period if you just want to learn how to run specific apps.
So why is pricing in red? Well, public cloud is easily the most expensive way to get started with homelabbing. The free tiers are great for running one app at a time, but if you're looking to do anything more than that, you'll need to open up your wallet. I hesitated to mark all but "space" green here; while capacity and performance are top notch, you really need to be mindful of how much you use. If I could add one thing to my Amazon wishlist, it would be a homelab tier that dumped everything on the lowest tier equipment without SLA guarantees for a deep discount.
Lightsail might be the closest thing to the "homelab tier", as you can get started with a Linux machine for $3.50 a month. The price scales with resources required, but is probably one of the more turnkey options on the market.