Hi Helen, Welcome to the world of gardening! I hope you find it as exciting and wonderful as the rest of us do! As an easy read, but with great information, you might want to try a book published by Martha Stewart Living several years ago called "Gardening 101." There are some great hints, tips, and information in the book, with great photos as well. I think a lot of your questions will be answered there. You can find it on Amazon and often times you’ll find it on eBay.
When adding compost or other amendments to my soil, I don’t necessarily ‘remove’ anything.. I’m simply adding to and in. If you’re starting fresh with a new bed, you can add a 3-4" layer of compost to the soil and turn it (mix) into the old soil using a shovel. (My Mom always used to call that ‘double digging’) Margaret taught me a year or so ago when she was doing the radio show, "Homegrown," the three C’s of soil amendment: Compost, Compost, Compost. It’s the best thing for poor soil.
My experience with mulch: Depending on the type you use, you can either add a thin layer to give it that ‘freshened’ look or you can remove the old and replace it. Good wood mulch however will begin to decompose and that’s beneficial for your soil, so I have ‘fluffed’ the old mulch to allow better air circulation and added to it. for a fresh clean look. Stay away from mulch that has ‘color’ added to it.. it doesn’t look natural and I’m a bit hesitant about the chemicals in it.
Best of luck! Congratulations on your new home and your new garden adventure.