If you need immediate help with farming, a good rule of thumb would be 1 legendary farmer or around 4 beginning farmer to every 25 tiles for plump helmet, year-around. Beginning farmers can support one dwarf per tile with year-around plump helmet and legendary around 3 per tile, without fertilizer and with average harvests. Though that's assuming you're brewing some of them for booze.
Each dwarf eat twice a season and drink four time a season.
Most efficient method of producing foods and drinks I've found is to have quarry bush or sugar pod made into dwarven syrup for food, they outperforms plump helmet rather handily, but need processing and cooking, and either pigtail or plump helmet to brew and hopefully keeping dwarves from eating them.
If you don't mind boozecooking, then brew plump helmet and pigtail, and cook them with a seed to make big stack of food. It can be a bit fiddly, but it's pretty much the maximumal efficiency you can pull off with farming. Animal husbandry is actually worse in term of food acreage to edibles, but can be less fiddly, particularly with birds, and offers leather and bones.
Though judging from your problems, you probably didn't set it to be planted year-around through season settings, or you're having issues with barrels of seeds. Latter's fixable by never using barrels for seed stockpile.
Even beginninger farmers should be able to support a major fortress handily, at least with large fields and some investment into infrastructure ( still and kitchen and stockpiles, really ).
As for your question about ideal farmer to plot ratio, I believe I've mentioned 25 plots to 1 farmer earlier for legendary farmer, you can manage with 40 plots to 1 farmer for anything other than plump helmet and pigtail due to growth length ( It assumes 1 planting a day, though, my farmers can do 3 or 4 a day once they get there, but I prefer to minimumize assumptions ). I'd recommend at least 2 farmer at minimum, and roughly 5 plot for 1 beginninger farmer due to slower planting rate.