How can I get from London Heathrow airport to Picadilly tube station?

Take the Picadilly Underground line from Heathrow to Picadilly station. Since the run starts at Heathrow, finding a seat wont be a problem

When is this? Now? Next week? Next year?

From Heathrow board the London Underground Piccadilly train which will take you to Piccadilly Circus. Exit and walk to your accommodation.

If there’s time before your trip make an effort to purchase and read the Rick Steves London guidebook. Lots of practical and helpful information.

Thank you. The trip will be in 3 weeks.

How much luggage? Which terminal? Will you be able to handle it on public transportation?

If so, then the Piccadilly Line is your best bet. Direct trip with no changes.

If not, take the National Express bus to Victoria Coach station and then a taxi. Once you get to the NE bus, the driver loads and unloads your luggage.

Piccadilly Line is really no problem with a reasonable amount of luggage. We just did it last month.

The TFL journey planner is a useful tool. It will show you multiple ways to get to your destination (bus, tube, train, etc.) and the cost. You can also specify preferences, such as minimize walking or fewer transfers or other accessibility requirements (such as escalators, no stairs, etc.).

https://tfl.gov.uk/plan-a-journey/

Taken that line many times from Heathrow. Easy, and ok with luggage. Many people on that line doing do.

Follow signs to underground. Clearly marked.
Easy to tap with Apple or Google Pay,or credit card. Just make sure you use same for tapping out.

does your tube journey fall during the November tube strikes?

Thank you all for the valuable information. I really appreciate it.