You can literally run a MUD server on a toaster. More specifically, a 486 or Pentium would
not be a good fit, but literally anything else would work. :D
The only thing you need is good internet. If your internet connection doesn't tend to completely fail (a small bit of latency and the rare crash shouldn't be the end of the world) then you're honestly good to go.
If you want to run this on a server, you're looking at around $10/mo for something decent, and if you scout around hard you may be able to get something for less. Google Compute Engine quietly let you have 600MB of RAM and 1GB of bandwidth per month for free, for example. :P
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Your profile mentions PHP and Node.JS. Of the two, Node.JS is probably the better choice to build something like this with - PHP's network/socket handling has a few sharp edges that make it occasionally fall over, and for a social project like a MUD, you'll get death-by-a-thousand-papercuts in the form of "...PHP?!" all the time, so there's that as well.
Obviously Java would work fine too; Node's advantages over Java in a context like this are lower grammatical verbosity and zero compile time.
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The first thing I'd recommend is poking around to understand how to do both telnet and websocket based networking.
Websockets will handle modern browser clients and cover 99% of a fledgling MUD's connections. Telnet will handle the die-hards who, if they come back, might stay for a while :P
Start with telnet first: you need to decide how you want the text UI to work. You can leave telnet out until you have everything else doing interesting things, but I strongly advise having at least a basic understanding of how VT100 emulation works from the start (while you're still in the design stage), or whatever you build may be extremely difficult to get working inside telnet.
Some web MUD clients just wrap a VT100 session hosted on the server with some websocket trickery and do things that way. That's a good way to do things, because it means people who want to stick with telnet don't really lose anything.
Websockets is just a networking system and is mostly fun to work with; to get started just find a library you like and tinker with it.
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As for gamedev, I recommend studying existing MUD systems, not with the intention of drowning yourself in how they all work (which will be disasterous), but to get an idea of how they structure their world info - what's where, how navigation works, etc etc.
Ultimately there are (AFAIK) few gotchas and MUD development is quite simple - rooms are connected to other rooms, and things happen - but it's a good idea to think through how you want to architect how rooms connect together so you can eg easily get at the bigger picture, and think about how you want interactions and cause/effect state to be maintained and associated with players.
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