However, if you had to choose one chain sharpening system, would it be something like the Timberline or would you choose an electric bench grinder such as this one from Garrett Wade . . .
First: Welcome to A.S.!
There are many ways to sharpen a chain. Personal preferences, skill, cost, workspace, etc. all factor in to this decision. You have to find a system that works for you. This usually means trying a few things, or having someone show you something that makes sense.
My main chain sharpening system is an electric bench grinder, but it cost substantially more than the plastic one you referenced, and it is a totally different tool. I like it and it works for me. If your budget is more modest, other options should be explored.
I have not tried the Timberline sharpener, but from comments in this thread, some of it's advantages seem to be: modest investment ($100 +/-), small to carry or store, don't need a shop or electricity, usable in the field or at home, repeatable results, etc.
Disadvantages . . .?
The one thing that has stuck in my mind ever since I read about it is the sneeze factor. With an electric chain grinder, you have to be extra careful that you don't accidently grind too much off...one mis-timed sneeze and you could ruin a good chain.
Not a realistic factor. If your sneezes are that devastating, what could happen when you are holding a running a chainsaw or driving a car?
The bench grinder is faster once you get it all setup compared to the timberline but you also have to remove the chain. . . I have never used any other bench grinder so I wonder if a Oregon grinder would be easier. . . I carry three to four extra sharp chains for both my saws so that lead me to want a bench grinder.
Nice to have a side-by-side comparison. Good point also about the difference between on-the-saw-sharpening and bench sharpening.
If you only have one chain for your saw, tools like the Timberline, or periodic file touch ups can work. A lot of people also like the Granberg File-N-Joint for about $30 (LINK:
Bailey's - Granberg File-N-Joint Precision Filing Guide). I tried the Oregon version when I first started sharpening my chains and got very good results and it helped me to develop filing skills. It was relatively slow, but I only had one or two chains to sharpen so that was not a big issue. These tools also work off of the saw if you chuck a spare (or scrap) bar in a vise and mount the chain and tool on that.
The Oregon 511A grinder that I use is faster to set up and to sharpen multiple chains. It uses larger diameter wheels and has a more powerful motor, which is especially helpful when cleaning up a 'rocked' chain (but not so powerful that it will cut my chain in half if I sneeze!).
Philbert