Bruges and Ghent via train from Amsterdam

Can someone please advise me on whether our first stop/overnight stay should be Ghent or Bruges?

Been there done that so your first overnight should be Bruges, which is the further point from Amsterdam (that is what I would prefer), then you can the train about 30 minutes to Ghent on your way back to Amsterdam.

You would buy the train ticket that has one stop going from Amsterdam to Brussels where you get off and change for the train to Bruges. Coming back you should buy Bruges to Ghent and then Ghent to Amsterdam separately.

This is the website you can use to buy your tickets directly from the rail operator
https://www.belgiantrain.be/en

From Amsterdam to Antwerp or Brussels, where you have to change trains for Gent/Brugge (and vice versa) you have the choice between the high-speed Thalys and the less-high-speed Intercity, which takes some 45 mins longer. Advantage of the Intercity is that it is an unreserved train, with your ticket valid for all trains running that day, which makes your travelling more flexible.

You want to think about your housing and luggage handling factors, as well. While local rail in Belgium is fast, cheap, and needs no reservations or advance purchase, both cities you named have a famous old-town that is a distance from the rail station. Most people take the cheap and easy local busses, but you should use Google Maps to see where your hotel is in relation to the train and the old-town. Many trains from Brussels to Bruges can have "commuter" luggage racks only, which can be annoying for long-distance travelers. If you can get your Amsterdam hotel to store your large bag, and bring a smaller one, it may be pleasanter for you.

You have made your nights-out clear. But I personally would add days to see a bit of Antwerp and (if interested in art museums) Brussels, as well. But a day in each of Bruges and Gent is reasonable. Note that Bruges is VERY crowded with tourists. Check closing days, especially because St. Bavo's in Gent is open seven days.

I personally do not associate Bruges with Amsterdam, but a huge number of posters on this site see them on the same trip to Europe. It is not a reason not to go, but note that Bruges is not "close" to Brussels. You might wish to look at the Belgian rail website to see some typical train times. (It will also make you feel good that there are so many trains EACH HOUR that make the trip!)

If you plan to see Grand Place in Brussels, note that Thalys goes to Brussels Midi/Zuid, which is the wrong station for Grand Place. But Thalys includes a single free ride on the many long-distance trains that stop at all three Brussels stations. And you can board/exit the trains to Bruges at any of those three stations.

I have sometimes had to wait in an annoying slow line to buy a local Belgian rail ticket from a HUMAN agent. There are some reports here that American chip and PINS MAY now work at Belgian ticket MACHINES, but I haven't been for a few years.

We did something similar
We had a very small window so we booked a Thalys from Amsterdam to Antwerp, changed to Belgian Rail and went to Ghent first. We stayed at the Hotel Carlton, about 400 yards from the train station.
The proprietors of the hotel are excellent guides and were able to visit Ghent the rest of the day.
The next morning we went to Bruges, stored our luggage at the station and went sightseeing.
That afternoon, we retrieved our luggage, boarded the train to Antwerp, where we transferred to Thalys for the remainder of our trip to Amsterdam. We used Rail Europe to make our purchases for the tickets - you can also look at other websites. They may have been a bit more pricier for parts of the trip, but it was easy to coordinate it from one website and the tickets arrived before we left on our trip.
Yes it was a very quick trip but there were things we wanted to see in both cities (Adoration of the Lambs in Ghent and the Bruges Madonna). Our time was limited but were happy to have been able to make the trip. We planned what we really wanted to see in both cities and the personnel at the hotel were happy to help us and even arranged for bus tickets in both Ghent and Bruges.
Good luck and have fun!

I prefer Ghent to Bruges, but based on your itinerary, I agree with the initial poster to overnight in Bruges. I find Bruges to be a bit overwhelming (and over rated) during the day, however, Bruges in the evening and morning (until 10-ish), is beautiful. When you make your way to Bruges, check in and enjoy the evening. After a nice AM stroll, head to Ghent en route back to Amsterdam. Although, don’t be surprised if you end up spending the night in Ghent after a few hours there.

Do I understand correctly that you only want 1 overnight for visiting those 2 places?
day 1: From Amsterdam to either Bruge or Ghent and stay overnight.
day 2: travel from one to the other place and in the evening go back to Amsterdam?

If this is the case, Why not just choose 1 place and stay overnight?

If you have a lot of luggage, it's a good idea to leave most of it in A'dam and just pack a small overnight bag for Belgium. That will make it much easier since as someone already said, you'll need bus/tram from the train stations to the historic centers. In order not to have your bag with you during one of the 2 days, you would need to travel first to town A, drop your bag at your hotel, then travel to town B for the day and return to A to sleep. Spend the next day seeing A and pick up your bag when you're ready to leave for A'dam.

I don't think it much matters logistically which town you visit first or where you spend the night. I prefer Ghent, very romantic after dark, but I haven't been to Bruges in the dark so I can't compare.