You can make a first order approximation by using typical WiFi ranges in combination with two free space path loss calculations.
802.11b/g has a typical indoor range of 150 feet. By calculating the difference in FSPL between 150 feet and 1812 feet, the approximate antenna gain requirement can be determined. Using an on-line FSPL calculator, we find 73 dB vs 95 dB of loss respectively for 0 dBi antennas. So your antenna must have at least 95 dB - 73dB = 22 dBi of gain.
This is a first order approximation that assumes the stock WiFi antennas have 0 dBi of gain, the normal working range is 150 feet, the window coatings do not present any additional losses, and there are no other attenuating effects in the path. Given all of this, adding another 6 dB of antenna gain (28 dBi total) for good margin would put you at a reasonable starting point.
An antenna such as this one would meet the requirement. Don't forget adapter cables and keep them as short as possible as these too will introduce losses.
Regarding the power usage requirements, here is a nice site that catalogs the power required for various WiFi access points. Based on this data, a budget of 15 watts would be generous. If you leave it on 24x7, it would use 15 watts * 24 hours per day * 365 days per year = 131.4 kilowatt-hours per year. According to Electricity Local, your residential electric rate is 0.0984 dollars per kilowatt-hour. This puts your worst case operating cost at $12.93 annually. That is well within the budget of even the most frugal grad student!