I've been making a fairly standard arrabbiata sauce for months, and I'd like to expand the number of sauces I can make.  However, many of these recipes involve cheese and/or milk, but I'm sadly lactose intolerant and would prefer to avoid these ingredients.  What others sauces could I be making, and what pasta should I use with them? 
 Tomato Sauce Putanesca Pesto (omit parmesan) Bolognese (meat sauce) Squash Puree (maybe with sage) Olive oil infusions (fresh herb/garlic/chilis/lemon zest) Roasted Red Pepper puree sauce etc  