It depends on the airline. Some like Southwest will just go up as it gets closer, unless there happens to be a sale that applies to your tickets.
But the odds of getting a "reduced price" are pretty slim. There is a time point, usually about 3-4 weeks out where prices will start to go up across the board. That way the airlines get more money from last minute business travelers who will pay whatever (within reason). Most vacations are planned out in advance, with business trips being last minute.
Better/cheaper is a matter of preference. Spirit can be pretty cheap, but you have to pay for everything. You pay to print your ticket at home, you pay more to print it at the airport. You can bring a purse/backpack with you for free, but need to pay for carry on, checked luggage, snack, etc. So if you will ship everything or wear just the one outfit your whole trip (please don't do this) it can be cheap. But when you add up fees, its costs just as much as other airlines. Southwest is usually a good middle of the road option, still competitive prices, but usually really good service. Jet Blue usually falls in that same class. The legacy carriers, United et al tend to cost more, and offer less. As
@DisneyJoe said, check out the airline search engines.
Kayak will often show you a chart of their confidence level of how prices will trend, helps you to guess if prices will shift or not. Skycanner will show you a tool to see the prices to travel the whole month. That helps you to see if it's cheaper to shift your plans by a day or two.
www.google.com/flights lets you see/book separate tickets which may be vastly cheaper, but also risk you being stuck if you have a delay.
Start playing around now to get an idea of options and how the search tools work to see what you like best. No one tool is perfect, some will find random results that others won't, and other have great features that really help.
Thanks for mentioning.