Kitchen grease on walls- what do you suggest?

I moved into an apartment about 6 months ago and am finally getting to the kitchen. My landlord has given me permission to paint and will provide what ever I need. The kitchen is paneling and over the years no one has cleaned it, the area around the stove is the worst with grease. Should I put kilz on the paneling first and then paint? What type of paint would you suggest I use ?
Thank you

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