Other than how you feel about a company, what ratios, metrics and historical trends do you analyze before purchasing a stock?

I'm analyzing and comparing Restoration Hardware (RH) and Williams-Sonoma (WSM). I'm trying to figure out what are some good indicators within company finances to determine if one is better than the other.

Whether it be Assets vs. Debt, operating cash flow amounts, stockholder equity amounts etc.

Trying to pinpoint specific things to highlight to help assess which company is better to invest than the other. I'm working on a report for my Accounting class in my MBA, and I really have no clue about stocks/investing other than if I like the company.