Giverny logistics

Luggage is an issue; if you are spending the night then your hotel should hold luggage before and after check in. There are virtually no lockers anymore and I am pretty sure St. Lazare is not a station with left luggage facilities. Bercy doesn't have them either. Most of the other mainline train stations do. There are luggage services in Paris. I think your best bet is to arrive first thing before the tour buses and before the first train from Paris; buy tickets ahead.

Be at the entrance in the morning before it opens with tickets in hand, if you can. I would go to the house first, then to pond. When I was there this past September, it was my third visit and I was shocked at how crowded it was. Besides the tour buses, the big river cruise ships drop off their passengers as well. The tour groups do have a separate entrance going right into the pond area, so as soon as you have finished at the house, head over to the pond, saving the rest of the garden for your way back. There was a line about 30 minutes long to get into the house by mid-morning.

If you buy your ticket in advance, you can enter through the group entrance rather than wait in the queue.
http://giverny.org/gardens/fcm/ticket/

Why not back to Paris in the evening? Probably more fun than Vernon (admittedly, I did not stay long to explore it) and an easier shot down to Arles from Paris.

We visited in June 2015. I bought our tickets online ahead of time and printed them at home. This allowed us to go in the "back" entrance closest to the pond (the first entrance we came to upon leaving the parking area where the bus from the train station dropped us off). We literally walked right in - no line. We completely avoided the ticket line at the house. We went to the pond first (we were there within an hour of opening) and were glad we did. It was not too crowded yet and we were able to enjoy the amazing garden there in relative peace. We then proceeded to the garden by the house and to the house. Entering from the garden area, we did not have to wait in line to tour the house. Before we left I wanted to take one more walk through the pond gardens. That was a mistake. By that point (late morning/early afternoon), it was literally wall to wall people. You were shoulder to shoulder and could not enjoy the amazing space. I would far rather tour the house in a crowded setting than the gorgeous peaceful pond area garden.

Granted, things may have change since then, but that was our experience at the time.

Sorry, I do not have any information on lodging and such.

One more comment ...
Without a car and given your plans to travel to Arles the following day, I think it would be more convenient to stay in Paris and just visit Giverny as a day trip. You wouldn't have to deal with luggage and the trip is under an hour. I felt Giverny was an easy day trip from Paris.

Laura has the right idea. You are just tying yourself in needless logistical knots if you stay in Vernon. It's an easy day trip.

I doubt there will be any way to avoid the crowds at the garden.

When we went to Giverny, we picked up bikes outside the Vernon train station and biked to Giverny--it was a very pleasant ride. We biked all around Giverny that day as well, which was probably my favorite part of the outing. As I recall, we arrived right around 11 or so, but weren't able to get tickets to enter until after lunch. Yes, there were plenty of other people there enjoying the gardens as well, but I don't remember it being overly crowded (we were there in late June). We had no problem taking pictures that weren't full of people. My general opinion is to enjoy the crowds--everyone is there to enjoy the same thing, so why not make some connections? Isn't meeting strangers supposed to be a huge part of the experience of traveling?

As far as an overnight, I'd suggest either staying in Giverny or returning to Paris. We spent a small amount of time exploring Vernon and were not impressed--we'd original planned to stay and have dinner there, but ended up having an apèro and coming back on an earlier train instead. There's not a lot to the town and we (3 women, early 30s) felt a bit uncomfortable. Granted, it was the end of a workday, so it may have come alive had we waited until evening.

As far as luggage lockers, you can look at the sncf website and see if specific train stations offer them. Last year I had no problem using them in several train stations. If you did rent bikes, I'm sure the bike rental place would likely let you leave your bags there as well.

Thank you to all posters for valuable information. We've bought the gas masks... now where to get the stink bomb!
Definitely tickets ahead. We've decided to stay in Vernon, checking in mid-day and going for the evening hours, when group tours should have vacated--this was a suggestion from one of the tour guides who has a lovely blog https://eur01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fgivernyimpression.com&data=02%7C01%7C%7C042a8075db564e30471308d58b593fd5%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C636568137790690251&sdata=6y9G3BeoMWg4BsD3zjBC%2FBmjX8GmFac7CL9vieUo%2FQw%3D&reserved=0

So that helps with luggage. The next day is travel intensive--to Arles. I hope we can do the bike ride suggested; it sounds terrific.
I did try to find luggage facilities on the SNCF website, but did not locate that info.

Merci, Cynthia

Please note that on May 9th there is a national rail strike in France so you may need to make other arrangements
See following site for the days of the strikes

https://www.thelocal.fr/20180316/french-rail-strikes-here-are-the-37-days-to-avoid-travelling-by-train

YIKES! re train strikes. Thanks so much for info. Cynthia

we were there in june 2017, we bought tickets prior and arrived early, and it was crowded as soon as we got there and got in.
the reason why it was 'crowded' ( eg: difficult to move around) was the pathways inside the garden are narrow and most of the paths that form the garden were blocked off. so the visitors are restricted to the main paths which don't necessarily cope with the quantity of people. that said we did find some space near the ponds.
hope this helps.

We did it as a day trip from Paris. It was a LONG day, but really nice. Sounds like you have the right idea to just stay in Vernon since you'll have your luggage to contend with. Once we arrived in Vernon via train, we went to a supermarket to pick lunch food. Then we walked back to the train station area to rent bikes (questionable quality of bikes) and had a blast biking the route to Giverny. We stopped and had a picnic lunch at a little park area along the river near an old mill (can't remember the name, but it is in some of Monet's paintings and would be hard to miss). I'm not very athletic but I still didn't find the biking too hard.

By the time we actually got to Giverny, it was early afternoon. We had advance purchased our tickets, so we were able to skip the lines and walk right in to the pond area. As others have mentioned it was crazy crowded. BUT, we saw the pond, went to the house and gardens, and then later went back to the pond area. By this time the tourist groups had cleared out. We hung around and were able to enjoy the ponds almost to ourselves for at least 30 minutes. We didn't leave until the guards made us:) It was so beautiful and at that point quiet! Hope you have good luck like we did!

keep in mind that trains to/from Vernon are at Gare St. Lazare, whereas trains to Arles/Avignon are at Gare D'Lyon on the other side of the city. Give yourself enough time to either take the Metro or a cab/Uber between the two stations if you are staying in Vernon overnight and taking the train back into Paris in the morning. Since its morning rush hour the train from Vernon also may be crowded (I don't recall there being reserved seats on that train).