1. Who are you?
If you don't answer this question within three seconds, you will lose the visitor. Your logo is the first thing that indicates who you; your H1 tag is the second. A good H1 tag adds to the aesthetic and UX of the homepage while contributing to the keyword density from an SEO perspective. Look at the great example from a growing Austin-based IT monitoring company below. They do this well.
You've answered the question of who you are, but now you have to convince a visitor that you have every right to be practicing in that industry. Your credibility badges, notable clients, honors, and awards should be in a place of visibility so your site exudes expertise and qualification.
3. What makes you better?
People like to compare, but they're not always thorough in their research. Often, a few points about what makes you better is enough to make a visitor to look no further. If they do look further, they'll know what you claim to be your differentiator. AT&T U-Verse does this well with their Gigapower page: "...a 100% fiber-optic network that delivers
both blazing fast Internet speeds and an enhanced TV viewing experience." Sure, Google Fiber is also doing this, but very few other competitors can make this claim.
Answer these three questions with concise and visually appealing content, you can be certain your conversion rates will go up.