Your question really all depends on what you want to do. I would want at minimum a graphical multitasking 32 bit OS like OS/2 2.11 or some type of BSD, I don't think there are any Linux versions anymore that will run on a 386. OS/2 2.11 would at least let you run multiple DOS programs at the same time, without crashing. And you're going to be limited to DOS and Win 3.11 era office suites, so like Word Perfect, MS Works, some very early version of MS Office. You might be able to get away with running Warp 3 on a 386, that would get you built-in networking with the fix-packs applied and give you a few more options with respect to multimedia but as to multimedia on a 386....you aren't going to be doing much of it. No movies. No Mp3 files. You could play the hell out of games from that era but forget much of the modern internet, you'd be limited to text-based email, text-based newsgroups, and maybe using Lynx as your web browser to browse a very few web pages that will work with it. You could play MOD files for music. There is still a lot you could do with a 386 as far as basic office productivity but your interaction with the wider world is going to be limited.
486-100 your options are a little better: you could, if you are brave, play around with editing postage-stamp quality video at 160x120, maybe 320x200 if you have specialized hardware. You could fart around with 3D graphics, if you can find older software or content yourself with Povray and other freeware that will run on an old Dos/Win3.1/OS/2 system. You could do image editing so long as you are sticking to images that are 1024x768 or less, you'd probably have to use 15 or 16 bit color depths though. I still don't think you would have enough CPU to run MP3s, so MOD files still for music for you, or compact disc audio with a CD player (same goes for 386, I guess). Your internet situation on a 486 will be much the same as on a 386. If you want to cheat and VNC into something like a raspberry pi 3 or other tiny PC you could surf the modern internet in a window. I think there may even be a VNC client for OS/2. Gaming on a 486, you would have all the options you had on 386 plus the 486 era, and since you've got a really fast 486 you may be able to play some early Pentium era games (Diablo, Quake if you don't mind it running at max 15fps, and so on). You'd have to dual-boot to Win 95 for Diablo, though, as I don't think there was a DOS version.
As long as you're ok with primarily text processing (basic office stuff) and you don't need to really interact with anyone else OR they are cool with you sending them RTF files or plain text or maybe CSV for spreadsheets, you might be able to get by. But I wouldn't want to seriously work like this. If you're an eccentric writer and you really really like your 386, that's the ideal situation as far as being able to produce useful output that might actually earn you a living. Otherwise....forget about it.
The 486 spanks the 386 in a lot of ways, especially the late era 486s like the DX4-75, 100, 120 and the 5x86 133 *however* having said that --- in the modern internet era a 386 or 486 is outclassed by the most humble of systems. It is like Homo Erectus is better than Australopithecus until you drop a Homo Erectus in modern NYC and give it a simple task: it will probably suffer a breakdown 😉
Don't get me wrong, the late 486 era is one of my favorite system types, but you need to have realistic expectations. You're not going to be able to hop on Youtube, Facebook and Amazon with it, or listen to Pandora Radio.