$$$. Figure out what you like by going to nurseries and look at yards around you area. Budget - yes, you will probably blow your budget once everything starts flowing, but that doesn't mean you have to buy the most expensive plants or materials. Get some help - even if they don't help dig, friends and family can offer suggestions and they will be the ones who will be in your backyard enjoying the landscape.
What would I do? Replace the fence, dig up the grass, or at least dig out the weeds and reseed, plant a border garden around the perimeter in front of the fence, maybe add a water feature and an arbor or pergola. BBQ GRILL - definite necessity! But that's just me.