It may be possible to do your first two years of school at a community college, which may be much less expensive, and then transfer to a four-year institution to complete your degree. If you want to do this, be sure to check with the school's advisors to be certain the community college courses meet the four-year school's requirements. You should be aware that many Engineering departments have their own admissions requirements in addition to those of the college or university of which they are a part. Some schools offer an Engineering Technology degree which requires less math than an engineering degree, but may not qualify you to become a P.E.
Once you've got the BSEE, it takes another four years (typically) of work experience, and some examinations, to become a registered Professional Engineer.
Be very careful if you try to go to a tech school! Most Accredited (4 year) Engineering and Architecture programs require your core courses to be taken through a school with a matching accreditation. So, you may be able to squeeze some Gen Ed (English, Math) courses out of a Tech School, but don't count on anything else!
In Ohio, it is possible to have a Engineering Technology (2 year) degree and still become a P.E. It takes 8 or 10 extra years of in the field experience, which must start
after you receive the degree.
As far as what to choose, good luck!
An Engineer does the design and spec work that a Journeyman or Master electrician installs, with the help of an Apprentice. If you really like math, and are good at complex formulas, Engineering may be the route to go. If you like to work with your hands, and trouble shoot things, Journeyman or Master may be the way to go. If you just want to show up and get bossed around, you may want to be an Apprentice, or "Electrical Technician".
If you know someone (close to you!) who is an Electrician or Engineer, ask if you can shadow them for a day or two.
Good luck!
-Dan