If you use the TFL Journey Planner, it'll let you find the best answer for your given time and day or travel. You can use the Travel options & accessibility advanced search to do things like minimise changes, minimise steps (if you have lots of luggage) etc
The quickest way will normally be to take a fast train from Gatwick to London Victoria, then a Victoria Line underground train to Oxford Circus, then a Bakerloo Line train to Paddington. The change at Oxford Circus is a cross-platform one, so no steps. You'll probably be fine to take a normal Southern service, there's little point paying the extra to save a few minutes on the Gatwick Express.
Alternately, if you want to avoid all steps, you can take a Southern Train to Victoria, then 36 bus from outside the station to Paddington. This will take 15-30 minutes longer, depending on traffic, but has no steps, and one fewer change.
You could take a Thameslink service to Blackfriars and change to a circle line train, but it'll take ages, and getting to the underground platforms isn't that easy with bags. Thameslink to Farringdon then H&C/Circle is another, that's a little quicker on the tube, but Southern/Victoria/Bakerloo is probably quicker and easier.