Train station name in Budapest

From wikitravel:
There is a railway station called Ferihegy (the original name of the airport) connected to Terminal 1 via a covered footbridge. Passengers from Terminal 2A or 2B can also reach it by taking local bus 200E to the stop called "Ferihegy vasútállomás" (8 min). Bus tickets are available in airport terminals for HUF 320 at the newspaper vendors, or HUF 400 if you purchase directly from the bus driver. Half-hourly suburban trains run westwards to Budapest-Nyugati pályaudvar via K?bánya-Kispest and eastwards to Monor via Vecsés and Üll?, though it should be noted that these suburban trains are operated by the Hungarian rail operator MÁV, and by no means included in the HÉV network. Suburban trains are recognized by their Személy label while long-distance trains use other designations. Travel time to Budapest-Nyugati is 23 min. A single ticket costs 365 HUF and can be bought from the ticket vending machines at the station, though local travelcards (which you can and should buy at the newspaper vendors at the airport unless planning to go by taxi everywhere) are also valid . Do NOT assume that it's always best to get off at Budapest-Nyugati even for the city centre. Nyugati is located in the north central part of the large city centre and depending on the location of your hotel, it is in fact often quicker to get off the suburban train at intermediate stations: for example, if you're staying in the southern part of the city centre (for example, but not only, the Gellért hotel), you should take a suburban train to K?bánya-Kispest, then change to Metro line 3 to Kálvin tér and finally a short tram ride to the hotel, since the Kálvin tér area is located quite a distance from Nyugati to the south. Similarly, if you're staying near the Keleti railway station, you should take a suburban train to Zugló and change to local bus 5, 7, 7E, 173 or 173E.

The above options require 3 connections -the bus from the main terminal, find the HEV train, and then take another bus or train to? That same 200 bus from the main airport terminal ends at the Blue Metro (possibly one station up, there is construction) which is then a 15 minute subway ride to the main interchange at Deak Ter. You can get to the airport the same way. You also should be able to buy a 10-pack of transit tickets that lower the cost to about 280 huf/per. Door to door this way for us last year, including getting cash and transit tickets at the airport and riding a second Metro to Bath Ter and walking to our lodging under Fisherman's Bastion, was barely an hour.
You also could pick a meeting place that is convenient for all, without you having to take a roundtrip to the airport.

Thanks Sarah and Larry, It sounds a little complicated for someone just getting there after a long overnight plane ride. We will be staying in a rural area in the hills on the Buda side of the River. The closest train station to us is Deli-pu. I think maybe we will just have the resort (Petnehazy) send a pick up for our friend at the airport. It might be easiest for someone who has never been to Budapest before. We can then work out the train/bus/metro travel when we meet up with each other. Thank you for your help and insight.

Amy- That Deli Pu station is also the last stop on the Red metro, which would be 4 stops after changing from the Blue Line at Deak Ter. This is essentially the same trip we managed last summer after an all night flight (left home 3PM, left Philly Airport after rearranging first flight at 5:20, arrived in Ferihegy at 2PM local time) and had never been to Budapest before (and in fact, we only began travel abroad in 2009, this was only our 3rd trip.) There was no problem at any point (other than make sure you validate your ticket properly when boarding the airport bus, the transit police think this is agood palce to catch violators, we were questioned 20 seconds after the bus pulled out, but we had known what to do) The connections I described are easy, and everything is well marked. The Budapest Transit System has an excellent web page at bkv.hu.en I see that your hotel has excellent directions posted, including public transit. This might be the one time to risk a cab, from Moszkva Ter Metro Stop (penultimate Red Line station before Deli pu), to avoid two additional transfers. Taking a cab from Moszkva Ter would minimize the chances of a severe fare rip-off by a cabbie, a known problem in Budapest. And it should take no more than an hour to get there from the airport.
This also has the advantage of avoiding two groups trying to meet somewhere in a large place (such as the train station) when one of them has been up all night. Enjoy the trip, this is a great place!

Be aware that last year they changed the airport name to Budapest Liszt Ferenc International Airport.