One thing that's certain, the Rays and their fans are in good hands. Despite the Rays bumpy economic conditions, they are arguably the most well ran team in the game. So rightfully so, even being in the middle of January there is no rush when in comes to finding a first baseman. There are many options available even with time dwindling, however, there are many viable options that suit the Rays need as a first baseman.
Someone like Chris Carter might be available. The 2009 MiLB player of the year had a rough go about it in Triple-A Sacramento despite finishing off his Triple-A year (in August) fairly strong. The 1B/OF's value isn't as high as it has been in the past although he finished the year off strong in the majors hitting nearly .330 over his last 10 games while belting 3 home runs during that span as well. As RJ Anderson pointed out via twitter, it's interesting to see Andrew Friedman, one of the best GM's in the league, trade with Billy Beane, another fantastic General Manager. RJ also pointed to the fact that 5 years ago, many would not expect Friedman to be the better GM in the future. Someone else who I think would make sense in a Rays uniform would be Yonder Alonso, however the Rays have lots of tradeable pitching depth, which the Reds don't have much need for. Alonso, 23, like Carter has low value despite coming off a fairly strong campaign at Triple-A Lousville, but like most coveted prospects, the price will be steep. Alonso, the 7th overall pick in the 2008 draft, is currently blocked by Joey Votto, the reigning NL MVP who looks to stay in Cincy for quite some time unless talks go sour.
There are 1B options of the free agent market, and by all means there are many ways to find a first baseman, even in-house options such as Dan Johnson, Leslie Anderson, or even Sean Rodriguez are possibilities, but as a fan of the Rays, it's known fact that trusting Friedman is the way to go.
Note: My name is Dave Gershman and I am a columnist for Beyond the Box Score and SPANdemonium. I also scout the NY Penn League at Hudson Valley, the Rays Rookie Ball affiliate. Hopefully, I will be contributing information and scouting reports when and before the season gets underway. You can follow me on twitter @Dave_Gershman