In any case, I'm glad you've taken it seriously enough to exercise and make some changes.
I live in a rural state and half the people here are at least an hour and a half drive from a gym, so we recommend walking. This is a great state for walking--dramatic scenery, wide open spaces, seasonal changes, wildlife. So that works, too you just need to enough of it.
As for cutting out fats, the main ones you need to eliminate are trans fats that make processed food shelf stable. That means chips, cakes, pies, cookies, or anything else kept shelf stable and contains fat. It also means avoiding most margarine (unless the label says no trans fats) and solid vegetable shortenings like Crisco and imitators. Yes, butter and lard aren't as damaging as those things.
You also have to get pretty savvy about reading labels, they throw hidden sugar in everything. Sugars themselves end in -ose. Sugar alcohols generally end in -ol, like sorbitol and xylitol. They get metabolized into sugars in the gut along with a lot of gas.
Good luck, it's a lot to take in. It can be done, but it's best done one step at a time.