these are the ones I can think of that actually satisfy the two criteria that you listed:
FTE, ezQuake, DarkPlaces, QRack.

no server: fodquake
no server list: directq, proquake, joequake, quakespasm/markv/etc

there are other engines of course, but the majority lack server lists - even qrack stretches that.
there are even more that haven't been maintained in years that I've completely overlooked. like tenebrae, or telejano, etc... but I've overlooked them...

fodquake is a decent enough qw client, and has a server browser, but lacks any server support.
directq is supposedly a decent enough engine, but lacks a server browser.
joequake might be a candidate, but its been a while since I heard anyone mention it and I don't have a copy myself and am too lazy to do anything about that.
fitzquake derivatives (including quakespasm) are decent enough if you want a fairly vanilla experience, but they're vanilla enough that they lack a number of convienience things like a server browser... their focus is generally on playing singleplayer than competitive multiplayer stuff.
qrack only supports nq, its server browseer requires you to manually enter servers iiuc. it also retains nq networking and thus requires firewall shinanegans to actually get it to work correctly as a server, so I should probably have not bothered listing it at all... its just a bit pathetic to only be able to list 3 engines that match the criteria.
ezquake only supports quakeworld iirc.
fte and dp both have server browsers and can both connect to either nq or qw servers. fte provides presets that allow you to easily select between reliably high framerates, faithful appearance, or realtime stuff. dp kinda looks a bit goofy on the lower settings, and tends to get half the framerate too (disclaimer: this is my experience as the main guy behind fte).
fte is awesome. what do you mean I'm biased? lies! 

For multiplayer help you may get better answers at http://quakeone.com but be aware - it's a MP-dominated forum so you'll get a lot of trash-talk and tantrums. 

no server list: ... proquake

Seriously, Spike? 

bah, fine. you got me. I don't mess around with other people's engines often enough.
I guess that means that you need to break stuff more so that I have more of a reason to test against your stuff. :)

I'd still rate DP over proquake for 'good server creation options', if only because DP(like qw servers) can automatically subscribe to a master-server. there's also the whole server-side port forwarding issue.
iiuc DP's server browser also beats your proquake server browser on account of it being able to calculate actual pings. imho ping times are quite important when you have a choice of more than 3 servers.
either way I guess your latest version beats qrack - certainly the version of qrack that I have... bah, now I annoyed r00k too. 

it's a MP-dominated forum so you'll get a lot of trash-talk and tantrums.

unlike the exemplar of patience and compromise that is func_msgboard 

 

Is FTE still the best option for playing online? 

If you really want to play online, jump into one of the MP-focussed discords. They will typically have some preferred client that they will help you set up and customize.

Generally speaking though, ezQuake is the common choice for QuakeWorld online. If you're not doing tournament play that enforces strict configuration thingummies then I'm sure FTE would also work fine, or fodquake... kind of comes down to which client-side features you prefer.

Not sure about NetQuake these days. I think the quakeone.com guys used to mainly use Qrack, and the "US Quake Community" discord does too.

Some discord links:
US QuakeWorld - http://discord.usquake.world/
US Quake Community - https://discord.gg/6U9RtT7
The Keep - https://discord.gg/DrWqYV
Quake.World - http://discord.quake.world/ 

XD