As far as cost goes, check out here:
https://www.mousesavers.com/2018-disney-world-room-rates-season-dates/
which lists the room rates at all the WDW resorts.
If you go in January and your visit coincides with MLK, at least part of your trip will be more expensive than other parts, because of the holiday. But that's probably the least-expensive of the times of year you're looking at. Presidents Week is, as you'll see from the chart, from from cheap. The rates in March vary, depending on when you'd go.
Crowds: Probably lowest the second week of January, although there's no such thing as "low" season anymore.
Weather: March wins that contest. Gorgeous weather in March. I had a perfect trip there this past March (end of 1st week)--slight rainstorm on departure day, but it was truly perfect the rest of the time. The worst weather I ever experienced at WDW (caveat: I've never been there in hurricane season) was in February. Cold, rainy, miserable, cloudy, and zero sun for an entire week. It's not always like that in February, but it was that year.
I used to go in January or February all the time, then for a couple of years running, several rides I really like were being refurbed in Jan/Feb. It's a very popular time of year for WDW to do their refurbs. Of course there can be refurbs anytime, but 2 years in a row with no Kali was it for me. We switched to March.
The wonderful thing about December is all the Xmas decorations. I mean, the castle itself is reason enough to go then.
But, you know, it's Disney. There is no bad time to go.
If costs and crowds are the biggest thing for you, go in January, but try to avoid MLK and the marathon.
HTH!