Ski trip to Zermatt

It's been a while since I've been to Zermatt, so I am a bit hesitant to make any specific
suggestions, but early March is a good time to go ; presumably after the European
half-term school holidays.

Lodging-wise, Zermatt has a wide range of options, but you're not early in looking for
hotels, so I would get going on the search. Do you want full-service hotel, B&B,
half-board? Location preferences? Note that walking a fair bit in European resorts
is not uncommon.

There are very few options in transport, assuming you don't drive. If your intent is to
go straight from Zurich Airport to the resort, then the big question is how much time
do you allow for regular processing + possible delays?

Hiring a guide is not a requirement if you are not a advanced skier, IMO. The skiing
is almost all above the treeline and you can see everything.

Between guides, lift tickets, fancy hotels, and gourmet dining, you are able to spend
a large chunk of change. Is that the type of recommendation you're looking for?

I was in Zermatt this past summer and stayed at the Hotel Alpenhof.

https://www.julen.ch/en/hotel-alpenhof/

I would stay there again. You can walk to it from the train station or they can pick you up.

You can take the train from Zurich airport to Zermatt. It takes about 3.5 hours with 1 or 2 train changes.

I don’t ski so can’t help with that part.

Early March is a great time to go!
The marked runs in Zermatt include yellow, unpisted "itineraries" that are patrolled and give you an off-piste experience without needing a guide. I spent a week skiing there in late March 2013 and some of those routes really tested my limits.
You'll have plenty to play with without needing to consider guides, and if you do, a half-day could be enough for a nice tour. Switzerland is much more expensive than its neighbors when it comes to instruction & guiding.

A decade later, any restaurant recommendations might well be obsolete, but I have fond memories of the hearty stews of Refugio Guide del Cervino, high up at 3,500 metres on the border with Italy.

There is a direct train to Visp every other hour from the airport (9:45, 11:45, etc). At other times, you will have to change trains in Bern. At Visp, you change to a train to Zermatt.

I don't think you need a guide unless you plan on off-piste skiing. If you want someone to show you around and help with your skiing, just hire an instructor for the day. Otherwise, the trail maps will show you around.

There are a ton of hotels in Zermatt. Some have halfboard meal plans (breakfast plus dinner) and are a good value. Restaurants run from the Golden Arches to very high end.

I was there in January and will be back again this January.