I am a beginning woodworker, and I'm thinking about buying a router later this year. I note that fixed base routers are somewhat cheaper than plunge routers, which is attractive to me. As such, I'm curious to know what one can do with a plunge router that you cannot do with a fixed base router (and some patience). Is the plunge mechanism really just a convenience / time saver? Or are there tasks that can only be done with a plunge router?
First of all, you are not necessarily limited to one or the other. You can get routers that support multiple bases - Plunge, Fixed, and Offset. If cost is an issue, either buy used, or get one that supports additional bases that you can add later.
As to the core of the question, one of the common mistakes people make with hand-held routers is making a cut that is too aggressive. A plunge router allows you to preset multiple depths, so you can quickly and accurately adjust the router between passes.
With some types of router work, such as inlay, you want the cut area to be very precisely defined. A plunge router allows you to reach your desired depth of cut without having to "angle drop cut" into your work.
While I do use my plunge router occasionally for 90+% of the time I use the fixed base. But there are tasks that are difficult if not impossible to do without a plunge base.
I agree over all with the LeeG's answer. But would add get one that will accept 1/2" and 1/4" bits, variable speed,and a minimum of 1 1/2 hp. Buy the best that is within your budget.
Having said all of that for years I used a $10 garage sale special, it did do the job most of the time but not as easily, now dedicated for the dovetail jig. Look around for a good used one some time they can be had at a very good price.