Gathering the number of Google results from a large amount of searches.
With any search engine you will be limited by number of requests and any way of outcoming those limits will be a gray zone of violation of end user agreement (and, eventually, you will get banned for some time, of course). You should be looking into Search APIs of known search engines, for example, Bing gives you 5000 searches per month for free which - for a proof of concept research - might be enough. Also, 5k/month will give you some 20-30k until summer, so your data set will become bigger while you will be polishing your idea.

Also, Google's free tier search is limited to 100 requests per day. Which gives you completely legal 3k per month as well. Combined (given, you treat Google and Bing results as equal) you get 8k per month.