With regards to getting to Paddington train station (for the Hilton there which I will look up!) you can take the Heathrow Express. Nice train. Goes straight to Paddington but costs £25. Takes 15 minutes.
If you want to save some money you can also take the Elizabeth Line (part of the Underground but a new line, costs a bit more) to Paddington for £12. It makes a couple stops and takes 29 minutes. Because you are getting on at the airport, it shouldn't be crowded.
The same trip on the Underground on the Picadilly line would require changing trains at Earl's Court but cost only £6. Check the Underground map if you are going anywhere but Paddington. The Picadilly line goes to King's Cross/St. Pancras if you are catching a train from there - such as the Eurostar to Paris.