The first, and only, experience I had with jig saws was using my dad’s vintage craftsman.
It looked pretty much like the one above, but it had the additional “feature” of being able to “steer” the blade via a twisty handle at the top. It was loud, vibrated, and had the cut accuracy of the average user of public restrooms. I hated using it.
Fast forward 25 years and I was staring down needing to cut out a 12″ circle from 3″ thick poplar for my first staked furniture build. I don’t have a capable bandsaw so my choices were rigging something up with a router or cutting it with a coping saw. Neither was a great option for me (i have router phobia).
I was wandering through the big box store and they happened to have a Bosch jigsaw on discount. Two minutes of in-store tool review searching and I picked up the JS470E and took it home. It stated on the box that it had 4″ hardwood cutting capacity, so I hoped that a a 33(.3333333…)% overcapacity would mean that it would actually work. I thought that I could at least get it close and then clean it up. It worked ao much better than I had expected.
The saw easily handled the poplar and left a clean (and square) cut. Took less than 10 mins to zip out the blank above and that included clanping and unclamping from the workbench. Technology has most certainly advanced in the last few years.
Don’t fear freehanding a circle too. Draw your line and just cut. You can always fair it out with a plane and spokeshave later. Even with a bandsaw you’ll have to do something to clean up the saw marks. And your circle diesn’t have to be perfect, just good enough to fool the eye.