BWI might be a good option, especially if you use a hotel shuttle to light rail to get to/from Inner Harbor and Preakness on race day. Given what you want to do, an Inner Harbor hotel would probably be more convenient, but doubt it would be within the price range.
Note that the MARC runs on weekdays, so you could also drop down to DC relatively cheap ($6 each way from BWI, $7 from Balitmore proper) on Friday.
I was at both the Derby and Preakness this year (reserved seats - not infield, though). Note that Pimlico is much less strict on what you can bring in than Churchill ^ , Barbara at the bar below the grandstand mixes the best Bloody Mary I've ever had ^ ^ , but the facility is an absolute dump

It's still a blast, and the triple crown is a fantastic goal.
The traditional connection is to take light rail to North Avenue and catch a connecting shuttle bus to Pimlico. A day pass is $3.50. There's also a shuttle option from the subway (that's what I traditionally use) that connects at Rogers Ave. MTA always does a special brochure and webpage with Preakness transit info.
MARC/Light Rail/Subway:
www.mtamaryland.com. DC Metro:
www.wmata.com