I don't think about keywords for SEO in terms of broad/exact/phrase match, so that's an interesting way of looking at it to me.

I also don't spend time worrying about singular vs plural, unless there's substantial difference in meaning between the two. I think current search engine algorithms are pretty good at discerning that "mountain bike" and "mountain bikes" are essentially the same search. Plus, if you have a page about mountain bikes, the natural way of writing content for that page is probably going to include both versions of the keyword. So don't sweat it too much.

"Cheap mountain bikes" is an altogether different concept because you're adding a descriptive modifier, so that would require its own optimization (just like if you were targeting "red" or "new" or "used" mountain bikes). Whether it's better to optimize for a phrase like this depends on a few things -- like if your mountain bikes actually are cheap, for starters, and whether that's the audience you want to attract to your site, and so forth. Generally speaking, when you're just starting out, it might be better to target phrases that are less competitive (which are often longer, but not always) because you probably won't have the trust/authority to get much visibility on more competitive terms (which are often shorter, but not always).

Hope this helps a bit.

Good advice by Matt McGee, I second what he suggested.

In response to your first question, my personal preference is to look at exact match data, as it gives you a better idea of search volume for specific queries.

As far as targeting numerous terms within a single keyphrase, you won't necessarily rank well for keyword = 'x' or keyword 'y', just because you rank well for 'x y z'. If you have some good content and optimization for 'cheap mountain bikes', it would be wrong to assume you're an authority on mountain bikes in general.

The more precise, or longtail, the terms are that you're targeting, the less challenging it is to optimize for them. Just keep in mind that if you want your page to be considered the go-to authority for any query, you'll want to target related queries in adjacent pages. Being an authority mountain bike site suggests that you'll have all sorts of well organized information on mountain bikes, including name brands, colors, sizes, parts; the whole kit and kaboodle.

Regarding your question on link building, I'm assuming you're asking about optimal anchor text terms. My best advice is to ensure you're site is as complete and well structured as possible before even considering hunting links. When you do start marketing your site looking for links, don;t be too obsessed with perfect anchor text; a natural link profile will have everything from 'bike store' to 'click here' and lots of 'www.minkadinkbikes.com'.

I totally agree with the comment about using keywords that target the audience you really want to attract. It's extremely frustrating to search through webistes that pulled up in the search engines, but they have nothing to do with what I'm looking for. It's not going to increase business, because even if people initially click on your site, they'll never return when they realize that you don't have what they're looking for. Take a realistic look at what you have to offer and what people might type into the search bar when they sit at their computer. Think about what words or phrases you use when you're looking for something. Often times, I enter questions or specific phrases, but rarely single words.

If you're talking about researching and choosing keywords for SEO purposes rather than for paid search, imo, it's important to switch Google's KWR tool over to exact match  mode. Otherwise, you really don't get a good idea of the potential keyword volume for any given phrase.

While it's true that when you optimize for a single phrase, you'll likely receive traffic on other peripheral phrases (similar to what broad match is) I still feel it's key to keyword selection to have some idea of the exact match numbers.

Regarding match type, agree with Jill 100% regarding exact match.  Keep in mind that it's the Google AdWords Keyword Tool, and as such is largely geared toward those bidding on keywords.  Broad match "allows your ad to show on similar phrases and relevant variations"; phrase match "allows your ad to show for searches that match the exact phrase" (but not exclusively, unlike exact match - e.g., if phrase match is selected "beautiful red widgets" will be included in metrics for "red widgets").  For organic search engine optimization exact match is the only way to meaningfully compare traffic volume between phrases.

Unlike Matt, I have spent time worrying about the difference between singular and plurals, even when the meaning of the two is basically identical.  There's a number of reasons to explore this:

• Most keyword tools, including Google AdWords, will display higher volumes for singulars than for plurals.  That is, if you're top ranked both for "red widget" and "red widgets" it's not uncommon to see a greater volume for "red widgets," even though Google reports that "red widget" should garner two times the taffic of "red widgets."  Sometimes this seems to be a flat-out data discrepency, but often it can be related to a different user intent when using the two different forms.
• Attaining high rankings for a singular does not necessarily mean high rankings for a plural, and vice versa.  Sometimes this discrepency can be quite large, and the task moving either forms of the keyword up quite substantial, so you do want to know which term to target.
• Singular and plurals do not necessarily convert at the same rate.  Which means, obviously, that - as per above - you want to target the right term.

What are typical differences I've found between singular and plural forms?

• Head term information queries favor the singular, head term consumer queries favor the plural.  A user interested in the characteristics of a mountain bike (general information about this type of bike) is likely to favor "mountain bike"; a user intent on purchasing a mountain bike is likely to favor "mountain bikes."
• Compound brand queries favor the singular.  A user is more likely to search for "nikon digital camera" than someone searching for cameras generically, who is more likely to search for "digital cameras."  When a model number or SKU is included singulars are almost exclusively used ("nikon p300 camera").
• Long tail queries tend to favor the singular.  The more words, the more likely the noun will be singular.  "Cameras" or "digital cameras" are likely queries for those objects, but "digital camera with 10x optimal zoom" is probably more likely than "digital cameras with...."

For all of these observations, actual results may vary. :)  Which is why for singular vs. plural keyword research, it's important to use real traffic data to inform that research as it becomes available.  That is, keep track of your traffic and conversions for similarly-ranked singulars and plurals, and ajust your targeting accordingly.  Examining your own data for keywords in traffic territory can also help inform targeting for singulars vs. plurals that are currently lower down in the SERPs.