In my own experiences, it is not a good idea to rank for any one word keyword these days. It is hard for a successful SEO and would not be profitable, either. It is recommended to be use more accurate 2 - 3 keywords relative to your niches. :)
Yes, i'm sure you are right but even keywords like "math classes" are probably among the most popular on the web. I know PPC can work but my question can you really compete with all the college websites to get on the first page of search...
Yes you can compete with that keyword, but it's not going to be that easy to out rank them, but you can try all you have to do is to have a good SEO plan.. But remember result cannot come overnight you must work hard on it and have a lots of patience..
First of all, you need to know how competitive the competitors are. The easiest way would be to see the KEI. If you are more pro, you can see the PR, Links, Cache Pages, how powerful the onsite optimization is with a glance.
You obviously can give your job to any company or freelancer. But remember whoever is doing your job need to research your keywords thoroughly. The proper selection can really helps you to stay ahead of your competitors. So make a proper plan about the keywords you want to target for your site.
yes it would be good to get SEO for your site, which can enhance your site ranking and make global presence.
If you look from local prospective it might not be that hard. The global competition for your keyword will be tough I agree but you are not targeting the whole world, are you?
I mean when I work in seo for a local company in Gold Coast, Australia they want to Target "Web Design" but as they hardly will have any customer outside their own state (they was building over 90% of sites on the same city). So finally we target "Web Design Gold Coast" or "Gold Coast Web Design" and ended up getting first page in three months and PPC advertising was lot cheaper compared to "Web Design".
Hope this will give you another point to think about.