That is a nice looking home, and what a backyard (for comparison mine is the size of the deck in this home's backyard). http://www.trulia.com/property/3015278688-630-9th-St-Wyandotte-MI-48192
Even though you didn't have a question, I assumed you posted this for some other reason other than just to share your thoughts with the world (unless you haven't discovered Facebook or Twitter yet).
Are you planning on using financing? If so, have you spoken with a mortgage loan officer to get pre-approved? That would be the first step.
Next you would want to make an offer, and if you have any slight uncertainty about what process entails I definitely recommend you use a real estate agent to do so. I know of a very helpful and patient real estate agent in Southgate, Tanya Klaffer of Real Estate One (just Google her name & company and you'll find her contact info), I've worked with her before otherwise I wouldn't have brought her name up. I am sure you will get other responses, so it's good to feel out at least a few real estate agents (just like you should do for loan officers).
If you are using financing, and aren't looking at doing any renovating/remodeling to the home, then you could use the traditional financing loan programs such as conforming (Fannie/Freddie), FHA or VA (if you are an eligible Veteran) financing. Down payments range from 0% (VA), 3% (conforming), and 3.5% (FHA), and of course more is certainly permitted. If you are looking at financing any remodel costs then there FHA has a certain version of their program, called the 203k rehab loan, which still just requires a 3.5% down payment (based on the purchase price + rehab costs) and another popular loan is the Fannie Mae HomeStyle Renovation loan program (which requires 5% down with most lenders).
Hope this has helped point you in the right direction.