Here are some helpful ideas for you
Delores, you will need to sand your cabinets first to get a good finish when you paint them. Do you have a small hand sander? It will definitely be a labor of love but beautiful when you finish.
You can use a mix of 1 cup of water, 1 cup of vinegar, 1/4 cup Dawn dishwashing liquid and a 1/4 cup lemon juice mixed together to remove the grease from the cabinets, let them dry and see if they still feel sticky and if so repeat the process. This works well on cabinets I clean on move out cleanings and good for cleaning many other things and cheap.
I've been painting for over 30 years... This bonding primer is the best I've ever used!! (click here for shopping link for primer) You do NOT NEED to sand before painting when you use this bonding primer. You just clean the cabinets, primer and paint.
I used General Finishes’ milk paint on mine. It was easy to use and required minimal prep work and very little hand sanding. I love the results! You can see my cabinets and how I painted them here: http://momhomeguide.com/my-painted-kitchen-cabinets-a-year-later/