Given the fact that a search engine deals with a broad range of topics, to promote a new search engine with google adwords, how do you choose keywords?
Having some Search Exclusive Keywords is a good idea.
Suppose the search engine is "Findforme". A website like this can have the keywords Find, Findforme and so on. Also, having some keywords like "Search Faster" or "Find Faster" should be able to help. Now almost all the time, a user will not look for another search engine in google as they are already satisfied with what google is providing them. Having various popular Search Term Queries (STQ's) as keywords in advertising for their search Engine may help in the ad popping up, although it may not have relevance to the user and the advertiser will end up paying a large cpc.
I searched some of the above listed keywords on google and these were the following results.
Search Faster: https://www.google.co.in/search?q=Search+Faster&oq=Search+Faster&aqs=chrome.0.57j0l3j62l2.2701j0&sourceid=chrome&ie=UTF-8
Hpoe this helps :)