Massachusetts has a lot of hills .... if you ever want to get off the bike path you will definitely want some gears. Western Mass has some actual mountains.
If all you really want to do is ride the same bike path over and over, a $100 single-speed from Walmart or Anywhere will be fine. On a flat path with only one small hill, no need for complexity. Save the other $300 so that when you finally amass $600-$800 you can get a bike from BikesDirect with a proper 50-34 crank and 11-32 or 11-34 cassette. It will be a while until there are many bikes in stock so no hurry.
Seriously, Anyone can build a cheap single-speed bike which will survive gentle use. No need to buy a brand-name bike when 90 percent of what you will be buying is the brand name.
Go used if and only if you know someone who really knows bikes---nothing hurts like getting all excited, getting your new used bike home, and finding out it has tons of terminal issues. If you can shop with someone who can tell whether a bike works or how much it might cost to get it working, then used is your best bet---particularly since you are willing to ride single-speed. If the derailleurs don't work, just jam them in the desired gear with the set screws and ride away.
of course, if you buy used, you will probably need minimum $100 for new tires and tubes, cables, maybe brake shoes, and probably a chain .... but since you can basically ride any bike that fits, you have a lot of options.