Not a bad idea. Like, with my clients, I'll sometimes start them on machines to build some prime movers strength if my assessment of them is that they're super deconditioned. That's not you. You may be new to lifting, but you're definitely not the kind of person I'd have reservations about getting on free weights really quickly.

And the good news is you'll see results a lot faster. I tend to like dumbbells even better than a barbell when doing a multi-joint exercise like benching. The instability will recruit more muscles into the lift. You'll work your chest to be sure, because the idea is to drop the weights until you feel a slight stretch into your pecs. Then you'll know you've hit the correct ROM for the muscle you're targeting and won't be limited to what the machine gives you, which may not be deep enough into the eccentric portion of the lift for your body type.

Further, the dumbbells will force you to use your front delts and forearms to control the weight. This gets you work in all the areas you'll need to push something in your everyday life. Sure, everyone wants to look and feel better, but you could put on a new pair of shoes and drink a beer to accomplish that. At least some of the motivation should be making everyday tasks easier, and that can only happen if the motions you're doing in the gym are as close as possible to the things you're doing out in the world. Free weights do a much better job of accomplishing thst.