Arriving Budapest via train from Vienna

Most of the trains, like the Railjet, go to Keleti station on the Pest side (east side of the Danube). I'd suggest a taxi from there to the Viking dock at the base of the Chain Bridge.

Consider taking a RailJet Express for getting between the two cities in a little over 2-1/2 hours. There are several departure times on any given day, but a midday option would be Train 61, which leaves Vienna Hbf at 11:40 and arrives into Budapest Keleti at 14:19. There's public transportation nearby, as well as plenty of waiting taxis to get you directly to the ship.

Kelenföld Station could work also, RegioJet goes there. There are no stations particularly near to the dock so one taxi ride is about the same as another.

WHICH STATION
In Budapest the station for the Hungarian and Austrian national trains from Vienna is Keleti pályaudvar (literally means Eastern Station). This is a beautiful old-world station and the principal station in Budapest. In Budapest the stations for RegioJet, the private rail service, are Kelenföld vasútállomás and Budapest-Déli pályaudvar. You will want to use Kelenföld. If you want to see an old-world train station take the national trains. If you don’t care if you arrive at something that looks more like an outside inner-city bus stop, take RegioJet.

GETTING FROM THE STATION
If your boat is one of the big companies like Viking the boat is most likely anywhere from just down river from the Chain Bridge to a kilometer and a half down river from the Chain Bridge. For some of the other companies I have seen the boats on a kilometer long stretch between Pest and Margrit Island, which begins about a kilometer upstream from the Chain Bridge. I presume the company will tell you where it is docked.
The implication here is that you are going from train to boat? It’s a shame because you do need more time in Budapest than the cruise affords you. At least two more days. But that aside; with luggage I would call a taxi, and I prefer CityTaxi https://citytaxi.hu/. Easiest is download their app as you can order the taxi on the app and it will show you where to stand to meet the taxi, taxi number, lic plate number, where the car is, etc. Just like Uber. The taxi will take your credit card since you don’t have Hungarian forints. From Keleti figure less than $15.00 from Kelenföld less than $20.00.
For those that are spending more time and travel “lighter”, you can use the metro or trams to reach your hotel. Tell me which train station and which hotel and I can give you a nice scenic route.

WHICH TRAIN
Doesn’t matter which train. Don’t be fooled by thinking the RJ and RJX trains are faster, they are not, but they are generally a bit newer. The EC trains are just as fast because the tracks from Vienna and Budapest don’t allow the RJ and RJX trains to run at their full potential. Pick the schedule and the cost, not the train type unless you want the perks of the RejioJet trains and they do come with some perks. The trip depending on which train will take 2:35 to 2:40 and that is dependent on the stops along the way more than anything else.

BUYING TICKETS
You can purchase tickets from the Austrian national rail line, OBB; but more often than not the tickets are less expensive from the Hungarian national rail line, MAV https://jegy.mav.hu/. Buy Rejiojet tickets from Regiojet https://regiojet.com/. Be sure to get a seat assignment for about 3 euro.

From Kelenföld, if you want to see the city, you can take the 49 tram to Fővám tér (30+ minutes) or the M4 underground to Fővám tér (less than 10 minutes) where you can use the 2/2B/23 Tram to go up the river to the boats (or walk down to the ones below the station).

From Keleti, you can use the M4 underground to Fővám tér (less than 10 minutes) where you can use the 2/2B/23 Tram to go up the river to the boats (or walk down to the ones below the station). If the boat is upstream fromm the Parliament the M2 from Keleti to Kossuth Lajos tér where you can use the 2/2B/23 Tram to get closer to the boats up river. If you want to stay above ground and ride a tram, then you take the M2 one stop to Blaha Lujza tér, then take the 4/6 Tram to Jászai Mari tér, then walk up to your boat if its upriver or take the 2/2B/23 Tram if the boat is down river from the Parliament. And there is another option using the M2 and M1.