Study abroad is a life-changing is absolutely amazing experience! A good time to travel depends on when you want to go and when you're available to go. If you are open, then any season would be great. Think about your preferences: do you like cold or hot weather? This will depend on which country you want to study in, and also where it's located. For instance, I see you're in Colorado and right now, it's winter. If you want to study in South America or Australia, for example, know that the seasons are different and its summer/hot. Maybe you want to experience a little bit of different seasons? Fall term would allow you to get some of that warmer weather at the end of summer, and cooler temps as the season changes. Likewise, Spring term would allow you to experience colder, winter weather, as well as the transition to spring/warmer weather. Summer is a popular option for many with constraints during the year or for shorter opportunities.
For financial tips, are you talking about scholarships/aid to help fund your study abroad, or saving money to live while studying abroad? Either way, I can provide some advice. If you need financial aid/scholarships/grants for studying abroad, look into your university, school (like school of social sciences, engineering, etc. The school your major is housed in), department (where your major is housed in), and major. For this last one on major, a simple Google search "[insert major] study abroad scholarships grants financial aid" would yield some ideas on where to get external funding in your community, state, or even world. There are tons of resources that are hiding, and you just have to dig, be persistence, and look.
Regarding financial tips to save money while study abroad or before you go, here are some ideas: get a job if you haven't already. If you have the summer to work, work as much as you can. Budget, and try not spend anything you can make yourself (like food). Sell stuff like clothes (to Poshmark or ThredUp for example) or books. I know coffee drinks are a big things during college, so learn to make your own -- going out for these yummy treats adds up big time. These may seem like small things, but they really add up a lot. Consider living on campus in a dorm or sharing an apartment while abroad, or living with a host family (and this will depend on which study abroad program you decide on). Do some research on expensive items in your host country, or things that may be difficult to find if you aren't going somewhere commonplace (like Europe). If you are a certain age (under 25 or 26 I believe), there are student cards that can save you tons of money on admission to tourist sights/museums/attractions, transportation, etc. I remembered when I studied abroad in Rouen, France, those under 25 were eligible for a free transportation pass! Talk about savings there.