I was unable to determine which state you will be residing in to provide you with more specific information. If you are in need of coverage between now and end of this year you can shop for private health insurance on websites like www.ehealthinsurance.com were you can receive free quotes, look at plan details and talk to a licensed agent if you need.
It is true that you can shop on state exchanges for private health insurance starting October (for January effective dates) but be sure to look at off exchange plans too especially if you don't qualify for premium subsidy.
Starting October 1, 2013 all states are scheduled to open an online Health Insurance Marketplace where you will be able to compare individual health insurance plans side by side.
Depending on what state you live in, information on plans and premium rates may already to be available to you. Four plan types will be offered through the state exchanges (Platinum, Gold, Silver, and Bronze).
If you don't foresee many medical expenses you probably want to be covered by a high deductible, low premium plan (silver or bronze) - meaning that your monthly fee for the insurance will be low, but you will need to pay a higher amount out-of-pocket (deductible) before the health insurance kicks in and helps paying for medical expenses.