Hi there,
I would stick to one high quality website with separate sections for sports and weddings. My only hesitation is the vast difference in the subject matter and the fact that wedding photography is such an important niche unto itself, but from an SEO point of view, one website is definitely preferable. You'll need to work on site structure and the branding of the wedding and sports sections to differentiate them and not confuse / alienate your potential clientele.
For the home page, I would go with the part of the business that is most profitable (I am guessing weddings?) and use navigation and SEO to optimise the sports photography page. PPC is a great way to get an influx of new traffic, especially if you want to do some conversion rate testing in the early stages, before you have a good amount of organic traffic.
I would consider creating pages for specific genres, even within your chosen niches. For example, a basketball page, including all the basketball content you've created like http://www.soobumimphotography.com/basketball-floor-remote/ and http://www.soobumimphotography.com/2013-nba-finals/
This section would sit under sports and be linked to from http://www.soobumimphotography.com/portfolio/sports/, along with a section for football, soccer, volleyball, boxing...
In terms of conversion, the contact form should be specific to the page it sits on - there is no need for a generic form with engagement and wedding options on the sports page, for example. I would tailor that to ask about the sport, the teams, the league (NCAA? High schoo? Pro?). I'd also really consider reviews or recommendations from your former clients, especially for weddings. They add trust, especially when paired with the people's actual photos. You can use Rich Snippets to include star ratings, and those star ratings can show up in search results: https://support.google.com/webmasters/answer/146645?hl=en
http://i.imgur.com/HMegwvh.png
I hope this provides some ideas for now. Let me know if anything is unclear.
Cheers,
Jane