Connecting with Rabbies Tour start near Victoria Station

Aer Lingus flies into Heathrow (T2), which would be fairly easy for you to use to get into town. And one of the fastest ways to get from Heathrow Airport to Victoria Station is to take the Elizabeth Line followed by the London Underground (Tube).

From Heathrow, head to the Elizabeth Line and take the train towards Abbey Wood. That will take you to Paddington Station (about a 30 minute trip). Transfer to the Underground at Paddington, where you would switch to the Circle Line (yellow) or the District Line (green) on the Underground. That will get you to Victoria Station in about 10 minutes. Here is a good map of the public transport system (with the colored lines) that will make it easier to visualize. https://content.tfl.gov.uk/standard-tube-map.pdf

Luggage should not be an issue on the Elizabeth line. What you could do if the luggage concerns you is to take the Elizabeth line to Paddington, and get a taxi from there to your hotel, which would alleviate the need to deal with luggage in the Tube. I've done it and it's not difficult but it depends on how crowded it is.

You can also route it yourself using TFL (Transport for London), which has a good route planner. Google maps will also give you a pretty accurate route as well.

ETA: If you are concerned about steps, you can look for stations/routes with "Step-Free Access" on the TFL site. With this, there is no step up and down to get into the tube (the Elizabeth line has no steps). Also there should be lifts available at Heathrow to get you to the train and at the stations.

The easiest way to Victoria by tube from Heathrow is Piccadilly Line to Baron's Court or Hammersmith, then a few steps across the platform for a District Line train to Victoria.

up into the Main Line station from the tube station, then walk through the station to the side entrance close to Platform 1 (next to the Belmond Pullman office). - that brings you out onto Hudson's Place, turn right.

Then from the PI to to Bulleid Way walk down Eccleston Square and turn right onto Elizabeth Bridge- that will take you straight there.

There are no facilities at what is really a former Coach Station. Nowadays it is mainly a parking garage for Victoria Coach Station across the way. Rabbies and a few other coach companies (mainly for the Continent) use it as a pick up point. It used to be somewhat better when Green Line used it, but now is not that nice a place.
If you fly into Gatwick Southern Trains or Gatwick Express will bring you straight into Victoria (the other side of the station, at the high numbered platforms).

From Heathrow, you could also take the National Express coach which goes to the Victoria Coach Station. The Heathrow Central Bus station is close to Terminal 2.

Victoria Coach Station is one block west of the Greenline Coach Station.

The Greenline Coach station is two short blocks to the Premier Inn.

From Heathrow, you hand your bags to the driver who stores it in the cargo hold. You get on the coach without having to deal with your luggage and it goes direct to Victoria Coach Station. The driver then hands you your bag and you go to your hotel. It's about a five to ten minute walk depending on how fast you walk.

From Gatwick, it's an easy train to Victoria Station.

You could also fly into London City Airport which is small and will necessitate some changes in trains.

Please don't consider flying into Luton or Stansted Airport. More hassle than any other airport. For ease, stick to Heathrow or Gatwick.

From London City Airport to Victoria is one train change- DLR [Docklands Light Railway] (bound for Stratford International) as far as West Ham, then District Line to Victoria.

West Ham has elevators to all platforms, as it is a major interchange with the Jubilee line and also the C2C National Rail line from Southend to London Fenchurch Street.

I just checked and was a bit surprised to see that the journey from LCY to Victoria was quicker than from Heathrow. Coupled with the fact that LCY is by some considerable distance the nicest and quickest airport to transit through I would go with a flight from Dublin to there, assuming that the fare is OK - LCY can command a premium mainly because of how much nicer it is than other London airports.