I would first try the top floor, close to the middle of the house. This will give the best overall coverage, especially if you will be using Wi-Fi outside the house.
If signal in the basement is too weak, you can try readjusting the antenna(s), or move the router the first floor.
Is there any way to find out the broadcast pattern of the router?
Does the orientation of the router matter?
Sent from my iPhone
Not really, it usually requires experimentation to find best results throughout the desired reception area. Just rotating the antennas can make a noticeable difference.
If you have an Android phone you can use the free "Wi-Fi Analyzer" app to test the signal throughout the house. It will also show you what frequencies your neighbors are using, to make sure you are on the best possible frequency. The lower Wi-Fi band is many times extremely crowded resulting in conflicts when moving away from the router.
Reception is many times more art than science.