Check garage sales. Get a used bike. The best bike I've ever had is my old mountain bike that I bought in the early 90s. I put smooth tires on it and bolted a Jandd grocery bag on the rear rack (so it won't fall off and nobody will steal it.) I put a shorter neck on it so I don't hurt my privates as I ride. The thing is indestructible and I can use it for bike commuting. When I bought it I chose it because it felt responsive, which means when I pedal I can feel the forward motion with each stroke. This was way more important to me than the bike being light and fast. It may not be fast in absolute terms, but the responsive feeling makes it feel fast.
With a bike like this, I don't worry about theft, I can ride it everywhere and use it for any purpose, with the exception perhaps of super gnarly trails, but I'm not into that.
If you really want a new bike, look into what they call a cyclo-cross bike. They're versatile like mountain bikes but a little more like road bikes. You might find one used, too.
Female, 5'3", 49, Starting weight: 163lbs. Current weight: 135 (more or less).
Starting squat: 45lbs. Current squat: 180 x 2. Current Deadlift: 230 x 2