I fall into the snob/prosumer hobbiest camp. There are few hobbies that you get to enjoy every day like coffee - so I didn't mind dropping the money. These machines will last years and some decades.
My favorite starter machine is the Rancilio Silvia. If you like to tinker, another $100 in the aftermarket will add a PID. But Brevilles are great machines. Home-barista (HB) loves the dual boiler one as the ultimate DB value buy.
It's true on the grinder. It doesn't matter how good the machine is if the grinder isn't up to snuff: grind, repeatably and uniformly, fine enough for espresso. There are plenty of advocates for a cheap lever machine and then the rest of the budget on grinder. There's a guy that has an old La Pavoni (~$200) and an EG-1 (a $4k grinder!!!) on HB.
I would look at Baratza's line up. I started with a used Vario from Ebay for $150. Good luck on the search!