depends on how deep you want to go. Obviously if you're only interested in checking top 10 then 200k isn't too big a deal but you'll need at least 100 proxies with Rank Tracker. If you want to go deeper than that, you can configure Rank Tracker to parse search queries w/ 100 results per page. Results won't be identical to 10 result per page queries, but it'll give you a pretty good estimate of where you rank. I would not go beyond 100.
I would divide the list by 20 and check each list once per week -- you could do 4 lists a day -- that way it will take you 1 work-week to do your entire list. Your results won't change much in a few days anyway.
You could also use the Google API -- you can go 64 deep with their api results...but I'm not sure how many queries you can do per day, I seem to recall there is no limit (it used to be 2000 but I think they got rid of that). Check with Google api docs.