On the other hand, it’s also worth noting that newer RAM generations are less and less susceptible to this kind of attack. Not because of any countermeasures, they just lose the data without constant refreshing much quicker even when chilled / frozen, so the attack becomes impractical.
So from DDR4 up, you’re probably safe.
If you’re going for a 3.5" HDD, then you’ll most likely have to look for a bit bigger form factor than TinyMiniMicro (Lenovo Tiny / HP Mini / Dell Micro series) - these computers can’t fit a 3.5" HDD.
If size isn’t a major concern, I’d go for the SFF variants of these computers - they are often cheaper than minis for same specs, but probably have a bit larger idle power draw and take up more space. As a bonus upside, you get some small PCIe slots in these computers, so yay for expansions.