I used to live in Victoria so this was pretty much my regular commute, it really depends on what your priorities are.
This is actually not bad by Tube as you are right next to St James' Park Tube station and can do a cross-platform transfer from District to Piccadilly at Baron's Court or Hammersmith, it will be £3.10 off peak with an Oyster or contactless and should be under an hour
Heathrow Express is quick to Paddington and my recommendation for the Tube-phobic, but getting there on public transport is not the quickest (crawl around the Circle Line or take the bus), so will not be much if any quicker than the full Tube option (you can also walk in about 45 mins and it is quite pleasant through the parks!)
A taxi from Paddington to St James' will take under 15 mins at that time of day, so if you time it right, end to end in about 40 mins
A taxi all the way from Heathrow should be about the same as the Tube/HEX option, and around £50 if you are lucky