I'm using Google Trends to research some terms right now. But I don't really understand what I'm looking for. I mean, I found some keywords that has high frequency. Which is great because that means people search for them. But that also means that there are lots of other sites already for that keyword. There aren't many people searching for unusual terms, but that also means there are less competetion and it will be easier to rank one's site for those keywords. Both have their pros and cons, so what am I looking for with keyword research?
Your observations are entirely correct. It is quite hard to rank good for the most popular keywords, people are doing that for years and years and put much effort into achieving good rank for them. While I think you shouldn't give up on them and slowly increase your popularity, you might also want to check and optimize for not so popular variations of the keyword and long-tail keywords. Search engines are more and more trying to meet customer demand and the algorithms seem to favor conversational searches more and more. People are starting to search for phrases, questions, whole sentences and the SERP's are trying to react accordingly, opposing to previously understanding each word as a stand-alone one. Best is to build a combination of your current and other relevant long-tail keywords and you should see an improvement