Old question, but it deserves a proper answer...
TL;DR Aluminum 1 AWG or possibly 1/0 if you expect consistent high usage, in 1-1/2" rigid metal conduit (6" burial depth) or 1-1/2" PVC schedule 40 (18" burial depth).
Panel size is listed as 100A. Based on comments of a load calculation of 76A, that would be correct. I am dubious about that (I expect it to be much lower), but let's assume it is correct for the moment, and use that as the value for voltage drop calculations. In addition, welder and at least some of the other key tools are 240V rather than 120V, so I'll use 240V for voltage drop calculations.
Note that you can (and generally should) use a 100A or larger panel as a subpanel, even if the feed is much smaller. For example, if you use a 90A feed breaker and 2 AWG aluminum wire, you can feed a 100A (or 200A!) panel. Larger capacity (current) panels are also larger capacity (spaces) panels, and you can always upgrade the feed wire and breaker if you use large enough conduit.
Minimum wire sizes (wires, not cables, 75 C rated) are 3 AWG copper and 1 AWG aluminum. For any significant distance, aluminum is almost always the better choice due to cost.
The Southwire Voltage Drop Calculator gives 4.46% for 3 AWG copper, 300', 240V, 76A and 4.61% for 1 AWG aluminum. Bumping up one size to 2 AWG copper gives 3.46% and to 1/0 aluminum gives 3.96%.
One thing that has changed quite a bit in the 9 years since this question was originally posted is electric vehicle supply equipment or EVSE, used to charge electric vehicles. If this garage is used as a garage and not just as a workshop then adding 20A - 30A @ 240V for electric charging is a common and reasonable thing to do. That could take a workshop garage from a much smaller real-world load - perhaps 40A - up to 60A - 70A or possibly more. Which in my opinion turns the 76A number from a way too high value to something quite reasonable.
Definitely go with conduit. Buried cable, which must be properly burial rated - you can't throw ordinary Romex in a trench - has to be 24" underground. PVC conduit only needs 18" and rigid metal conduit needs only 6", except under driveways. For a short distance this makes rigid metal conduit a very good deal as you can dig the trench easily by hand. For a 300' installation it may not matter so much because it will pay to rent equipment to get the job done in a day. But I would definitely trust PVC conduit in the long term much more than buried cable.
Conduit size will vary. A quick calculation on Southwire's site shows that 1-1/2" PVC 40 or Rigid Metal Conduit will do fine. You may be able to use a slightly smaller size, but a larger size will allow for 1/0 so if you start with 1 AWG and later need to upgrade you can do that.