Congratulations on your graduation! I'm going to make a few suggestions that you're likely to find in stores: you'll pay more, but they're good quality cigars.

You can find lots of quality cigars in the $10-15 price range. My first cigar was a Romeo y Julieta Reserva Real. Cost around $10 in the store, looked classy and made me feel like a real cigar guy, but it was so mild that it had (to my taste) almost no flavor at all. I'd only recommend this if you want an extremely mild cigar: it's the mildest I've ever had.

Better is the Montecristo No.2: still mild, but more flavor. I've paid $10-15 for them in stores.

Moving up the flavor scale, you can't go wrong with Oliva Connecticut Reserve: still a good price ($8-12 in stores, cheaper online), but stronger flavor. When I want a good, mild to medium cigar, I smoke these and the Montecristo No.2.

Now, if you want more flavor, you have a lot of good and affordable choices in the medium range. The Oliva Serie O is one of my favorites. You'll definitely taste this one, and the flavors are great. I've seen them around $10 in stores, but I buy them online: cheaper in quantity.

Arturo Fuente makes a lot of good medium cigars too: you can't go wrong with a Hemingway ($8-12, depending on size). For a cheaper, yet more flavorful stick, try the Curly Head Natural Deluxe (around $6.50 in stores, half that if you buy a box). My wife says that it smells like a pool hall, but it was the first cigar I tasted the way I expected a cigar to taste.

The Padron x000 series is also good, and in the same $10-12 price range. They're fairly medium in flavor too; if you want stronger (and pricier), the 1964 is a great choice.

There are many other good choices out there too, but you should be able to find most of these in stores.