Not crazy at all! We have painted several pieces of furniture. It is tedious but certainly within the realm of the average DIYer.

The furniture we've painted has all been raw wood, which we primed and then painted with a semi-gloss latex paint. Since yours is not raw wood, you should probably sand lightly first, then use a tack cloth to get off all the sanding residue. Actually, don't take my word for it, Google will be your friend on this -- or just ask at any home improvement warehouse where you plan to buy the supplies. The folks in the paint department at places like Home Depot and Lowe's are there to help with just that kind of advice.

Also -- I really like the look of mixed-finish furniture, not a matched set. In our bedroom when we owned a house, we had a light oak armoire and dresser, white painted picket-fence bed (that's one of the pieces we painted), and a pale yellow LL Bean bedside table (farmhouse look). Our walls were light blue with white trim, and our quilt was in shades of light blue, white, and pale yellow. It looked really nice, if I do say so myself. We were going for a farmhouse look, but even for other styles, I think mixing furniture pieces is prettier than everything being all matchy-matchy.