i think the less different knots you use the better off you are, especially for a beginner. learn to tie these knots perfectly and you will never have trouble with knots breaking or slipping.
1st you need to be able to make a loop knot. I like the perfection loop
http://www.animatedknots.com/perfection/index.php?LogoImage=LogoGrog.jpg&Website=www.animatedknots.com you also neet to connect flyline to leader and for this I use a sheet bend knot. it looks too simple to hold but i'ved used it for everything from bluegill to bass to steelhead to pike and never had it fail. the best thing about this knot is its small and slips easily thru thr guides. But if you prefer, use a double sheet bend to make it more secure.
http://www.animatedknots.com/sheetbend/index.php a line to line connection for tippet to leader is, i feel, your most important knot. you may have multiple line-to-line knots so they should be your best and strongest knot. for this i use the blood knot. may think it's too hard to tie but with practice i can tie it in 30 seconds perfectly 95% of the time. if it's going to fail it will when you give it a good pull just after you tie it.
http://www.animatedknots.com/bloodknot/index.php?LogoImage=LogoGrog.jpg&Website=www.animatedknots.com and to tie on a fly a simple 5 turn clinch is fast and simple. i've rarely had it fail when tied properly. i find no difference between the clinch and improved clinch when each is tied correctly.
http://meritbadge.org/wiki/index.php/Image:Clinch_Knot.gif the most important thing to remember when tieing any knot is to lub it with spit while the wraps are loose, then pull tight slowly. when secure give it a long, steady, hard pull to test the knot. if it survives this it will not fail except at the most extreme limit of it's strength.
like i've said if you learn these 4 you then can learn the countless other knots for special cases.