Michelle –
I don’t see any reason to wait and purchase a bin — or make your own — especially if you have plenty of table scraps ready to use. Many commercial bins are rodent proof, which sounds like it might be helpful in your area. And yes, burying table scraps will almost always invite rodents. I’ve attached a few links from several of our composting sites that will help:
https://www.planetnatural.com/product-category/organic-gardening/composting/
https://www.planetnatural.com/composting-101/
https://www.planetnatural.com/composter-connection/
One other suggestion. If you have a constant supply of fruit/vegetable scraps and not a lot of yard waste you may want to consider composting with worms. Here’s a link:
https://www.planetnatural.com/worm-composting/
Hope this helps!