Arriving in Narita late night, best options?

I recently booked a flight and am arriving in Narita (first time in Japan) and I found out that most of the trains stop running a few hours before arrive. For reference, I think I will be arriving around 00:30 but with customs and luggage I suspect I wouldn't be out of the airport until 01:00-02:00. I know there are taxis but my housing will be in Tokyo and it seems that taxi will be quite an expensive option. Is my best bet to spend the night at the airport? Although I'm not sure if that's even an option.

One thing to add is that I think I can cancel my flight for a penalty fee but there is another flight that arrives in Haneda at around 22:00 if that might be a better option as it seems closer to Tokyo. Any thoughts?

Sorry if this is a dumb question, but I have never traveled by myself and especially not out of the country.

Where is your accommodation in Tokyo? Trains may not be running, but there are express buses (limousine buses) that stops at or near your hotel.

Otherwise, you can book a room in a hotel near the airport or crash on a bench at the terminal.

If you even consider changing flight with penalty fee, how about staying in Narita?
It won't be so expensive.
These places are in Narita Airport.
https://ninehours.co.jp/en/narita/
http://www.apo-resthouse.com/english/index.html

If you do not mind, would I take you to Tokyo by car? I live in Narita and I can drive to Tokyo by car in an hour

Narita Airport is actually outside Tokyo.
Haneda Airport is in Tokyo's urban area.

Paul:
I recently booked a flight and am arriving in Narita (first time in Japan)
I think I will be arriving around 00:30

I recommend you check again
the estimated time of the flight arrival [ETA].

Landings and takeoffs at Narita Airport
are restricted during the very late and early hours.

Narita Airport [NRT] has three terminals.
Which NRT terminal are you expected to use?
(Railway stations are in Terminals 1 and 2, but not in Terminal 3.)

Buses connecting two or three NRT terminals
are available until around 23:10.

Courtesy buses of a nearby hotel
may not depart after midnight from NRT terminals.
(Some run not via Terminal 3 during the late hours.)

... (guest) :
These places are in Narita Airport.
https://ninehours.co.jp/en/narita/
http://www.apo-resthouse.com/english/index.html

9h nine hours Narita Airport is a capsule hotel near Terminal 2.
Narita Airport Rest House is a hotel near Terminal 1.

Paul:
there is another flight that arrives in Haneda at around 22:00

That too sounds late,
enough for a first-time visitor to care about transportation modes.
Nevertheless, when ETA is (about) the same during such late hours,
HND arrival can be better than NRT arrival
for you to find your way to get to your accommodation in Tokyo.

For reference, I think I will be arriving around 00:30 but with customs and luggage I suspect I wouldn't be out of the airport until 01:00-02:00.
I think you have that wrong - NO flights arrive at that time at Narita Airport - the airport is closed at that time - even with the recently announced extension to landing times, the last arrivals are around 21:30.
Are you flying to "Tokyo"? Tokyo International is at Haneda. Post the flight number - that will make it simple. From Haneda, get a taxi or stay at one of the hotels in the airport.

As an example, I had two people said they were arriving at Tokyo to the same airport five minutes apart. When I got them to tell me their flight numbers, I was able to tell them they were arriving at different airports and would not be able to happily meet at "Tokyo" airport.

Hey guys, I just want to apologize, you guys are right and I had misread my flight information. I was in fact arriving at Narita but I ended up getting the times mixed up, as in I would be arriving in afternoon. I was looking to change my flight at Haneda instead, but realized that it might be better if I just rested the night before and arrive in Tokyo the following morning instead. Also, I appreciate the offer USACHAN99, but thankfully it seems like everything will be okay. Thanks everyone.