Let's talk about what is probably the most widely used (by homeowners) furniture finish today: polyurethane. It has many of the advantages of varnish, with few of the drawbacks. Polyurethane dries more quickly than varnish, so you don't have to worry (as much) about dust settling in the wet finish. It flows better than varnish, so brush marks are more likely to disappear. Correctly applied, polyurethane is more durable than varnish. Many people, however, won't use it ... why?
The most common complaint against polyurethane is that it "looks like plastic." Well, the chemical structure (when dry) is very close to plastic, but the reason some people get that idea is from being told that a certain piece of furniture, such as a restaurant table top, is coated with polyurethane, when in fact, it isn't. Since they don't like the way the top looks, and they've been told it was polyurethane, they don't like polyurethane. Most of the ultra-thick finishes you see on commercial furniture (furniture exposed to the public on a regular basis) is a plastic, which, strangely enough, is why it looks like plastic.
If you take three identical pieces of furniture, finish one in lacquer, one in varnish, and one in polyurethane, no one is going to be able to tell you which is which without testing the finish with solvents.
One other complaint against polyurethane (mainly from people like me who work on furniture finishes) is that polyurethane is very difficult to repair, and many times difficult to remove when stripping furniture. Well it can be repaired and it can be stripped, so that bias just reveals how lazy (I admit it) some repairmen are!
Polyurethane lends itself to good results with a minimum of investment. It's its own sealer, and you don't need a fancy brush to get good results. Foam brushes give great results. Of course you can't use the brush but one time, but if you're going to put three coats on a piece of furniture, you won't need but three brushes at, say 89 cents each? That's a lot cheaper than a $15 or $20 brush, which you have to clean after every use. Remember I'm talking about the home owner, not the professional. The professional will invest in the good brush, and keep it clean, because it's cheaper in the long run. But for the do-it-yourself who's going to do one or two pieces of furniture in a year, shelling out $20 (or more) for a brush is ridiculous.
As with varnish, work with a small area (about one foot square) and then move on, overlapping as you go. Brush from wet to dry. In other words, brush from the wet area of finish toward areas yet to be covered. On table tops, do the edges first and then work from the middle of the top out to the edges. Never start a brush stroke at the edge moving in; you'll drag finish off the brush and it will run over the edge. Again as with varnish, don't over brush. Get it on the surface, smooth it out, and leave it alone. The few brush marks you leave will settle out if you don't keep messing with it.
When finishing turned legs, work around the leg, starting at the top and working down. When finishing square (unturned legs) work from top to bottom on all four sides at once. Do the edges of flat surfaces first, then work from the middle of the surface out to the edge.
Polyurethane is a modern, durable finish that is easily applied by the beginner, producing a wear resistant finish in a variety of sheens, from matte to gloss. As always, read the instructions on the can carefully. The manufacturer knows more about his product than you do, and they want you to have good results.