I have a 20' 2004 G3 HP.  I fish primarily on a lake of maximum 30' depth, mainly rock/weedy bottom.  What style/size anchor do you recommend?

I have got one of those mushroom ones.

Pluses, easy to pull up, easy to deploy, no to snag on boat.

Downside, in moderate/heavy wind or wake, it will slip(depending on bottom)

When I was growing up we had one of the "normal" ones that dug in a bit.

Pluses, once it caught, it did not move one bit

Downside, occasionlly we really got it stuck and had to go upstream, had to be real careful not hit the side of the boat with it.

Also, do you usually fish with a current?

Tri-fluted River Anchor  

i have a digger. works well in any condition. you can release the fluke angle with just a jerk of the anchor rope. downside is it is a liitle bulky. anchor rope payout is the most important with any anchor. depth x 3

I had a tri-fluted river anchor, emphasis on had.....

first day I was using it was when I had my father in my boat for the first time. he is a worm dunker so I anchored for him. I usually just let the boat drift or use the trolling motor. Well after fishing for about 30-40 minutes went to pick up and move. Could not budge the anchor, ended up having to cut the rope. Any thoughts on what I did wrong???

It happens with any type of anchor, something you just accept from time to time; in 35 years I've lost 2, 1 was last year.

Each type of anchor has its advantages and disadvantages.

Mushroom.  Little better than a hunk of metal.  Holds in light wind, but not in current.  Snags the least amount of weads.  Can be rinsed clean by just bobbing it up and down in the water.  It is what I use 99% of the time.

Forked anchor holds in sand, much stronger than mushroom.  With a 10 ft leader of heavy chain holds even better.  This is the standard for current or heavy wind.  Will bring large amount of weeds up with it and must be picked clean by hand.  I have one in the boat in case I need it, but have not used it yet.

Other anchor designs are more situation specific.