I live in a relatively small town and for my business, no other competitors are using Google Adwords. There is about 3 other competitors all of which have been around for 10-50 years. They get enough business from word to mouth and have not done ANY online marketing. I have been using Google Adwords Express for about a month now and have had amazing results with increase of business. I am realizing that I need to get away from the Express and start using the more advanced Google Adwords. If what I understand is right, I can have way more focused results and save an immense amount of money.

Due to me having completely no competition for the best keywords for my business, can I bid $0.01 and put high budget for the day. In theory no matter what, if the keywords of my choice are searched, my ad should always be at the top. If $.01 is not allowed, can I bid lower than the "First page bid estimate" and still show up?

Is this not true? Any feedback appreciated.