Need advice.

You can choose any style of bike within your budget for that type of riding. However, if you do plan to go from that onto the roads, at any kind of distance (say 30 miles/50 km or more), I'd suggest either a drop bar or flat bar road bike.

On a budget? we all have budgets, but how much is that budget? for some it may be $300, for others it may $3,000, so give us some sort of range to work with.

My initial impressions is that you start out as cheap as possible, perhaps buying a used bike, but buy a bike for under $300. Why you scream? because you said you're just starting out, most people who just start out quit after about 3 to 6 months and if you spend $1,200 or so for a bike you'll end up with an expensive piece of garage art if you quit. If you don't quit and love cycling then after about 2 to 3 years you can then go out and get a nice bike and keep the older one for when you need to go somewhere and lock it up, or for mucky days.