The questions you asked have been answered multiple times throughout BP. I would highly suggest searching "list source criteria" and "direct mail response rates" to gain some helpful insight. My favorite on the subject is @Sharon Vornholt as she has multiple blog posts regarding DM.
I'm going to write the following assuming you mean $1000 total - not $1000 per month. If you meant $1000/mth, just quadruple my suggestions. A list of 2000 names from LS will run you around $200. If you are running on a flat $1000, I suggest breaking it into 4 mailings to the same 500 people using standard postcards. Mail in 6 week intervals so you'll hit the same 500 people 4 times in a 6 month spread. This is recommended versus hitting 2000 people once, which would use the full $1000.
If you send 200+ postcards at a time, you get "bulk rates" which cuts postage in half. My mailings are out-of-state so it costs $.26/each or $70/250 cards. My printer charges $35 for the printing so I pay $105/250 postcards and I mail a batch every week. I break them into multiple campaigns of 250 and have 6 running at a time. Hence why having a list of more names than you can mail to is a forward thinking idea. Once you land deals, up your volume of mailings.