Drip/pour over coffee machine with burr grinder

I have searched the threads but can't see anything recent and I know things are constantly changing in the world of coffee.

After years of drinking coffee and using many different coffee machines, I have decided that my favourite brew hands down is the drip/pour over type with a medium ground bean.

At the moment I just have a Hario V60 or a cheap drip russell hobs machine from argos and a separate old burr grinder that is running out of steam anyway. I am looking for a decent machine that i can just hit the switch in the morning for it to grind enough beans burr style and brew two great cups of coffee while we are getting ready for work (I get very distracted in the kitchen if I spend more than 30 seconds in the kitchen ).

I don't mind paying up to 200 - 250 for a decent machine as have a gaggia classic and a nespresso (rank) that I will be selling off due to lack of use anyway.

Or is it a case that I should stick with the Hario and invest in a decent grinder (along with all that time spent in the kitchen each morning).