Im based in England so if some of my terms arent American, my apologies. If you have a look in any garden centre, Costco or Wall-Mart, you would be able to find miniature greenhouses made from plastic used for propogation and seedlings. These would be perfect for your seedlings on the window. You can also cheat a little by surrounding the front edge with tin foil to reflect a little more sunlight. keep the soil moist, dont let it get dry to the touch.
You will need a starter compost such as J Arthur Bowers No. 1. The salts and nutrients are low enough so the radicals dont bolt cause them to die from to fast a growth rate.
Your fortunate to be surrounded by oaks. Of all trees(certainly here in UK), they support more variety of wildlife than any other. Once your seedlings are ready to be potted on, find the best spot you can, afternoon sun for preference.
All the best with your window garden. are you growing flowers or vegetables. if you can find “F1” varieties, these might be most favourable.
let know how you get on – post some pictures here. it would be great to see