You were following too closely and probably moving too fast for the conditions. Your insurance will cover your looses minus your deductible. How you spend the money is up to you and any lien holder.
The reckless driving ticket is major. Going to cost you BIG TIME for future insurance. Many companies simply won't cover you with a reckless conviction and others will charge you double the rate of a clean driver. Make sure you hire a good lawyer to beat this one. At least try to get it reduced to a careless driving citation.