Consider an induction cooktop. You won't incur the cost of the new gas line.

Do you like the wall treatment? If not then I assume you will change it - I am not sure if it is wall paper or a decretive paint treatment. I like it when people express themselves in their kitchen, but if that isn't you, then change it. If you want to keep the cabinet doors, you could back the glass ones with fabric as seen in this photo: http://www.livingthecountrylife.com/homes-acreages/country-homes/16-farm-kitchen-features-we-love/

You could paint the cabinets - white, cream, blue, green - many options as I've looked at your idea book and you have some great examples there. You may want to do the island a different color. Beadboard backsplash is inexpensive and you could carry it around to a wainscot. You could take down some upper cabinets and replace with a country style plate rack / shelf somewhat like the picture below. I think Yield House has similar units.

The shelf above the cabinets will be a great place to display some farmhouse antiques - but do not clutter. Pretty china platters or pewter platers, baskets, stoneware or milk glass pitcher etc.

You have a lot of countertop - on a budget you may have to go with formica, but there are many choices and styles to choose from and some are very attractive. You could use wood for some of the countertops - farmhouse and economical. Ikea has some at a reasonable cost.

If you do not have any little ones to get into things, some lower cabinet doors can be replaced with curtain or shelves with baskets as seen in this photo from French Country Cottage blog - guest house kitchen. (Hover over photo to see full picture)