Best way to get from Heathrow to Oxford?

By coach. https://www.theairlineoxford.co.uk

The "Best" way to do this is by hiring a car and driver to take you.

The more practical way, and less costly, is what Badger suggested.

I had the same question in 2019 and this is the information that I received:
https://community.ricksteves.com/travel-forum/england/heathrow-to-oxford
It was very helpful. We simply went from our flight to the bus within LHR, bought tickets, driver put our bags underneath and we were off in just a few minutes. The bus ends in the middle of Oxford. Our hotel was just two blocks away. From Point A to Point B, it did the job.

National Express bus which takes about 1 hour from T2 and T 3 terminals. I believe they run about hourly 24 hours a day.

National Express only run every 3 hours or so. The Airline (run by Oxford Bus) as above is the more frequent service. National Express also sell the Airline tickets as a third party, but you might as well buy them direct. Ones bought through Nat Ex have a fixed travel time, those bought direct have flexibility.

Agree with the Airline bus recs! We did the Airline coach from Oxford to LHR and it was great. We booked ahead for a specific time since we were going back to the airport. It was early morning so I didn't want to deal with tickets in the moment, but we watched others get on and it was really easy to just tell the driver what ticket you needed (one way vs return, child, etc) and then tap your credit card. It was so convenient - we got on at the Westgate stop as that was closer to our Airbnb. It was 90 minutes almost on the dot.