which is cheapest and/or fastest way to get from Luton Airport to London (Coach or train)?

Depending on where you're coming from in London

Rail: First Capital Connect from Kings Cross Thameslink (and other stations), takes about 25 mins from Kings Cross, or Midland Mainline from St Pancras (fewer trains). Then free shuttle bus from the station up to the airport. A fully flexible return ticket is £22. There may be other, cheaper tickets, especially if you hold a railcard. Link: www.nationalrail.co.uk

Bus:
You have two options

Easybus- every 20 minutes to/from Gloucester Place/Baker Street, takes 1h to 1h 20, depending on time of day. They are claiming fares as low as £2, but I wouldn't necessarily expect to get them. www.easybus.co.uk

Green Line- Every 20 mins (daytime) to/from Victoria, it runs 24 h- less frequently at night. Takes 1 h - 1h45 depending on time of day. A return is £15. www.greenline.co.uk

National Express coaches can do it (one way) for £10. Or from £14 return.
Not fast - it takes between 1 hour 9 minutes and 1 hour 24 minutes depending on the time of day you will be travelling. Comfortable coaches though. Even the loos work (most of the time).
The prices are based on an under 59 year old travelling but there are extra concessions for over 60s, holders of Over 50 travel cards, disabled and also Children and Family reductions. Not a bad package.
I use them for Brighton to London and returns often. Take a good book with you and you'll be in Victoria before you know it.

Their site is:
www.nationalexpress.com

A not very user-friendly site so you will need patience.