Do you have a certain geographic area that you're interested in working? If so, I would start researching theatres in that area and see where you'd like to work. Polish up your resume and cover letter, and have someone (like a friend or professor) look them over. Some theatres will list on their website what email address you should send resumes to- if they don't you can always try the production manager. Tailor your cover letter to the theatre you're sending it to! If you're applying to different genres (like dance or opera) it can be helpful to tailor your resume as well, to highlight relevant experience.
You can look up job postings - there's a thread
here that lists a number of job posting websites. If you are planning on working in the same area that you studied, your professors may be able to get you introductions to folks hiring in that area. If you have connections from your internship, use them! Ask them if they are hiring, or if they would be a reference for you. It really helps to have a connection when you're applying to a new theatre- people will consider your resume more carefully.
Are you interested in ASM positions or SM positions? (Or both?) Are you looking for one full-time position all year, or are you willing to freelance?
Once you turn Equity, you'll be competing with all of the other Equity members in your area for those positions, so it helps to build up some non-AEA experience on your resume for a few years. Then, when you're ready to turn, you'll have the experience to get hired in those positions. Once you have started working, I think you'll get a better sense of how much experience you need before turning.
Re: finances. There's no one right answer for this. I would research the cost of living in whatever area you plan to work, and make a budget from there. If you live at home for a while after graduation, you might be able to afford to take some lower-paying positions while you build up your experience. If you are paying for housing, utilities, etc, you might need to look for higher-paying work, and/or supplement with a day job or other freelance work, like electrics calls. It's hard to budget as a freelancer - I found it helpful to create a spreadsheet with all of the work I had scheduled for the year and how much each job paid. Then I could see which months were going to be light and look for filler work, tighten my budget, and save up so that I had savings to tide me over.
Hope this helps!