Hello. Some corrections who has been through the process. Ancestry. Hungarian ancestry is a lot easier than any country I have heard of. My grandparents were born in the Kingdom but with Trianon lost in 1920 making them Slovaks. Hungary citz understands this issue and is actually a plus for you. It confirmed my Hungarian blood in writing by the consulate. You do need a beyond basic level of the language and you DO get an answer within 90 days of submitting from the Embassy. This is a law that they wanted to expedite. If you are American or Canadian your chances are much better as they know you are doing this for more emotional reasons and that you are likely to be more financially fit.
I did get a written confirmation from Embassy staff that I was Hungarian blood from my grandparents despite their birthplace being present day Slovakia. On the other hand Slovakian citz is pure hell as it takes years and endless paperwork. Residency and despite having a Slovak mother, they can be VERY difficult to work with and documented as one of the worst for granting citz in all of the EU even if you are blood descent. Been there and went through the insanity.
-Ancestry. I have one Hungarian ancestor.
Just having an ancestor isn't enough (60+% of Americans have known European ancestry), but Hungary is one of the most lenient countries with giving citizenship by descent back multiple generations. That said, this will require a years-long bureaucratic process and you will at least need to do a lot of research and cough up a lot of documents pertaining to this ancestor and all of them between you and him/her. Whether this is worth the trouble is your call. Note that Hungary in old times when most people emigrated to the US was more than twice the size as Hungary now, and they will probably refuse your claim if there's not an ethnic Hungarian name involved (I somehow doubt a Slovak name from a Slovak village would work). You will need some language skills or someone to help you just to get through the paperwork, and I've heard widely varying stories on the amount of Hungarian language you need to possess to meet the language requirement. Just be aware that the main purpose of their lenient law is to allow the Hungarian minorities living in neighboring countries to have an easy route to citizenship.