It’s tricky to make a recommendation as pretty much all the home lab stuff that people typically run can be done so on a potato, which is why RPis are so popular.

An N100 would definitely be a step up from the pis and meet your stated needs. They are super popular, in a multitude of formfactors so should be able to find something you like. But you may get the itch to upgrade further if you expect to expand or experiment extensively. Like any hobby, it’s generally easy to justify to yourself that you need to get that “next cool/better/faster/prettier thing” so such an itch may be unavoidable no matter what you get.

Instead of worrying about performance, as pretty much any modern miniPC should outclass a Pi, take a look at the specific form factors that are available. Do they have the expansion, networking you need? Can you stick this thing somewhere out of the way and not worry about it taking too much space or making too much noise? Are you comfortable with their level of support/warranty? Expect garbage/non-existent support from most of the miniPC specialty brands out there, which includes minisforum which I recommended in another comment. If you outgrow it, are you comfortable with it being e-waste/have a means of repurposing it?

While N100 is great for what it is, especially at a $200 budget, it can be limiting with its fairly small core/thread count if you expand beyond a handful of applications.

OP mentioned tinkering with multiple Linux flavors. A higher end cpu, with more cores and threads, would allow them to virtualize multiple instances on top of whatever other workloads they have and potentially not break a sweat while the N100 could struggle. While such an upgrade would be more expensive, price for performance will likely be significantly better if you can make use of it.

I’ve had good experience with the Minisforum MS-01, while it’s more than your $200 mentioned, it’s been worth every penny. Plenty of power for most homelabs and lots of nice features for future proofing (10gb, Ethernet, plenty of storage options, small but still usable pcie expansion slot) in a small form factor.

I’ve pretty much retired all my RPis at this point and my old Synology NAS is now just storage only with the MS-01 doing all the actual work.

Really don’t have a reason to migrate away from it for many years unless it died. Even then, you can create a promox cluster with them trivially to provide some redundancy.

They also have the a1 and a2 options for AMD but the a1 doesn’t have the same feature set and a2 is pretty expensive if you don’t need the extra power.

It’s what turns it from a children’s book into a horror story