Good for you!
If you're going to bike for more than just leisurely pedals around your neighborhood, I would go for a true road bike (the kind that has skinny tires). The bike you're looking at is more for biking a mile to the beach, or running some errands and such. In a bike event, most riders will be on road bikes. You don't have to spend a fortune on a road bike. If you're just starting out, borrow one if you can or buy one used on craigslist to make sure you actually like it first. I did my first triathlon using my husband's old beat up bike. It was actually a bit to small for me but was fine and then I bought one that fit better this spring.
Go to a bike store and let them measure you to tell you what frame size you are and that can help with buying something used. This is really important - my husband and I are the same height but our proportions mean that my frame size is bigger than his. There are some tutorials on-line that also tell you how to take your measurements at home. Once you know your size, you're much more likely to find something that feels safe and comfortable.
Don't be intimidated by clipless pedals, which may come on some used bikes you look at. You can always switch them out to regular pedals or pedals with toe cages until you decide whether or not you like it enough to invest in clip-in bike shoes and pedals.
FYI for a beginner, a 25 mile ride will be 1.5 - 2 hours so be sure to allow time to train for your ride. Sounds like a great thing to shoot for though - have fun!
ETA: I didn't realize that the bike you are considering doesn't have gears - definitely wouldn't work! You need gears! My newer bike has 21 but even 6 or 10 can work.