I agree with those that say 5x is a very good starting point. More and more it is generally accepted that the fish are not as tippet shy as was previously thought. However, too heavy of a tippet for a smaller fly will make it behave less life-like in the water. For dry flies, too heavy of a tippet will make drag free drifts harder, if not impossible, to achieve.
The three most important aspects in fly fishing are as follows, not in any particular order: 1 Presentation 2 presentation and 3 presentation. After that somewhere down the line specific pattern selection comes into play.
For streamers I would suggest going down to no less than 3x. Believe me, I learned this the hard way when I was starting to fish big streamers for big fish. By big I mean anything bigger than a size 6. Of course, you need to use a streamer and tippet sized to the fish you are after. I do not throw a big streamer on small mountain brookie streams. Out here we chuck big streamers on 1x, sometimes even 0x. When I am back in Pa. I do the same thing. It works.
For real small stuff, 18 and smaller, it is often necessary to go down to 6x, rarely 7x. I know that I will have many disagree, but, I fish Depuy's spring creek all the time and never use anything smaller than 6x. That is true for the Big Horn and Mo where tiny flies are the ticket.
Using 7x and smaller really adds to the stress that the fish go through. Playing bigger fish on light tippets is a skill that is good to learn, but work your way up (or down) over time. The lighter the tippet the more important it is to have a decent reel with a good drag.
BTW, it is good to learn to play big, strong fish on your trout gear. The way I learned a good deal was to fly fish for carp with my trout rods. Go after smallies too. Anything that will fight much harder than your average trout. That way, the first huge trout you hook and try to play on your fly rod will not be the first huge (relatively) fish you ever hooked. It is far better to loose a few 5 lb carp than 1 5lb brown! Beside, with carp you can learn just how much preasure you can put into a fish on a given tippet.
One more related point. I see this with far too many of my clients. Tie good knots, and re-tie them often. After a few fish, after no fish and a good snag that comes out. The more you re-tie your flies the less fish you will loose. I have seen far too many fish of a lifetime get away from poorly tied knots or knots that should have been re-tied long ago.
