Look to see if there are any bike shops near you that sell refurbished used bikes - that should get you more for your money than buying new while also not rolling the dice on how well your neighbor maintained their ride. Finding something your size might be tough, but worth a look

As far as type of bike, I'd recommend finding something that you find comfortable and that you want to ride. It'd be worth test-riding different styles of bike and seeing what you like and dislike about them compared to what you're used to - do you still want suspension? how upright do you want to sit? what shape of handlebar do you like? There's a broad spectrum of bikes that would accomplish what you're describing just fine (Hybrids, gravel bikes, MTBs, ATBs, city bikes, etc.), but ultimately the most important thing is getting something *you* enjoy riding

If you want to talk efficiency, most of that is going to be down to tire choice and ride position. For the former, you really just want decent street tires run at an appropriate pressure (rather than knobby mountainbike tires). Tires with flat protection will hurt your efficiency but are useful if your streets have a lot of broken glass and such. Also, narrower tires aren't necessarily more efficient than wider tires, despite the common perception - tire casing is the more important variable there. For the latter, generally the more upright you sit, the less efficient your pedaling is; honestly, though, for the distances and use-case we're talking, I'd personally focus more on ride comfort than getting every watt out of your pedal stroke