A Live One is a great intro in some ways but not others. on one hand it represents the various sides of the band pretty well and every song on it is one of their best. But on the other hand it's not a proper show so the flow is weird and it also draws only from 1994 recordings and includes some stuff that new listeners will find impenetrable (the 30-minute Tweezer is the main culprit here).
Phish have kind of a catch-22 situation where you can't always easily appreciate what they're doing unless you already know the songs but since so many songs are live-only you can't learn the songs unless you listen to the live show.
My general advice is to listen to a few studio albums and then when deciding what shows to listen to pick shows that heavily feature songs from the albums you know. That way you'll get some stuff you're already familiar with as you are also introduced to other songs they play during the show. If there's a song you particularly like look up the song on Phish.net and see what other shows it's been played in that look interesting and try those out.
Maybe my biggest tip is: Always listen to shows (or sets) in full when you can, but don't relisten to shows. At least not at first. obviously if you listen to a show and want to hear it again don't stop yourself. but don't force yourself to listen to shows over and over again as if they were regular live albums. Just keep moving and trying new things. This is the best way for quickly familiarising yourself with their catalogue while also continually keeping things fresh. I've been listening to the band for years, and I love the fact that if I want to hear a Phish show I haven't heard before there are *still* tons of great shows for me to choose from.
As far as specific shows go. Any shows they played for special events are always highlights. Halloween, new years, and their festival shows are three categories that you can't go wrong with at any era in the band's career (and most of these have been officially released). The original Live Phish series is also an excellent place to start. It was a 20-volume series of archival releases (Dick's Picks-style) where each band member picked their favourite shows to include and you can't go wrong with any of them. After those original 20 volumes the Live Phish series kept putting stuff out but they dropped the numbering system, but it's a good rule of thumb that if a show has been officially released it's probably a good sign that it's a great show.
some more specific recommendations:
New Year's Eve 1995 - super well rounded show. It's always one of the first people recommend and I don't disagree.
Live Phish 1 (December 14, 1995) and 2 (July 16, 1994) are both mostly normal shows where every song is a great version. Great starter shows for sure.
Live Phish 15 is their Halloween show where they covered Remain In Light. All the halloween shows are great, but if I had to pick one I'd go with this one. Unless you hate the talking heads, then maybe try Live Phish 13, 14 or 16 where they cover The White Album, Quadrophenia, and Loaded respectively.
At The Roxy 1993 (3 shows from feb 19, 20, & 21 1993) - very zany shows with lots of segues, special guests, weird covers, one-off jokes, vacuum solos ect. Feb 20 1993 is the best of the three if you just want a single show from this run. A great place to get a sense of their sense of humour.
Clifford Ball (August 16 and 17, 1996) & The Great Went (August 16 and 17, 1997) - Their first two festivals. Both are killer from start to finish.
Island Tour (4 shows april 2-5 1998) - the peak of their funky jam excursion mode. great shows to start with for exploring that side of the band.
Almost every Phish show ever performed is available to listen to for free in bootleg form (downloads: http://phishspreadsheet.com/ streaming: http://phish.in/ ), and the officially released soundboard recordings are widely available too. if you're piracy-savvy you'll have no trouble finding the official releases for download, though if you're a stickler for legal methods there are a bunch of classic shows on spotify. Phish's official youtube channel is also a great source for highlights from their current era.
A guy on reddit posted a "phish for beginners" write-up recently I thought was pretty good. he sums up their different periods pretty well and gives different recommendations than what I gave: https://www.reddit.com/r/phish/comments/9ot9ed/welcome_to_phish_a_guide_for_beginners/
Oh also watch the documentary "Bittersweet Motel". It captures them in their prime in 1997 and it's a pretty enjoyable rock doc even if you're unfamiliar with the band.