You can configure Syncthing for more ad-hoc, but it’s a little convoluted.

Try Resilio Sync - it has a Selective Sync feature that allows you to select individual files to sync in the moment.

I use Resilio this way to access my files at home - Resilio runs on a machine at home and indexes/shares the root folder on my NAS. Then from any device (including my phone) I can browse for any file and select sync. It will take as long as needed for the file size and network stability, but it will sync the file.

This is especially useful for media files, since I can’t exactly keep my entire library (4 TB) synced to my phone, but using Resilio I can grab any movie/TV show/music at any time.

Just don’t leave Resilio running your phone - it can be hard on memory as it keeps an index there, and it isn’t the most battery friendly app. So I close it when done syncing something.

What’s wrong with your keyboard?

In my opinion (others may disagree) a used Small Form-Factor (SFF) desktop like the Dell Optiplex series strikes a good balance of size, performance, and just enough room inside for a couple drives (I’ve actually added a SATA card and 4 laptop drives to one - more costly on drives, but gives me a small unit).

Plus they’re a decent price on eBay or locally.

The other option are the mini pc’s - these are very small, often have a very small fan (or none) so cooling limits how much performance you can get from them. But these are great for the light services you listed - cooling shouldn’t be an issue (my CPU doesn’t even bump from music streaming, and barely shows an increasing from video streaming with transcoding). Because they tend to cost similar to an SFF, and my space isn’t that constrained, I prefer the SFF with it’s performance advantages (including the ability to add a decent video card).

Because of their compactness, you can (usually) at best get a single desktop drive in a mini, and often they may only fit a single 2.5" drive.

Now the bad news for right now - both memory and drive prices are at a significant high.

Edit: One thing I forgot - both of these kinds of systems have low power draw at idle which is a big deal for self hosting. My SFF idles at 20 watts with an 8 TB data drive and 2 500GB SSD’s for VM’s. It peaks at 80 watts when converting videos.

First, if you want to stream video, having video on a NAS instead of the server may introduce a bottleneck. It’ll be your call as to how to address that (depends on your network performance, may not even happen).

I haven’t done the math, but I suspect an inexpensive Small Format-Factor desktop with an upgraded video card will probably work.

Streaming requires much less performance than one would think, especially if you carefully convert videos to formats your devices can easily handle (basically avoiding transcoding as much as possible).

I regularly stream from a 2019 i7 SFF with no video card, with transcode (for subtitles) to a 65" TV and that barely shows on CPU, disk, or network (gigabit).

Simultaneously converting videos, and copying files all over the place including sync with Resilio, Syncthing and running VM’s rarely causes video issues. I have to really push on the network for video to stutter.