Can't give you any advice about making pasta with your machine because I don't know which types of pasta machines are available in US...personally, I have a hand machine, but use it only seldom because I like more making fresh pasta entirely by hands. It's time consuming, but when you have a good practice pasta ends up much better. Most of all, the pasta rolled with a mattrel, being less smooth, keeps better the sauce and results tastier. The main problem is that you'd need a true Pasta mattrel, that is more than 3 feet long! I still have my Grandmother's, who was from Parma, but don't know if they're available also abroad....
In any case, the original recipe of fresh egg Pasta "Bolognese style" simply calls for these ingredients:
1 large whole egg each 100 grams (about 3.6 oz) white wheat flour, and a pinch of salt.
No water; no oil; no other liquids. No whole wheat flour or durum semolina-you can use them for fancy pastas, but NOT for the real "Pasta all'uovo"!
This pasta is the tastiest you can get, and the best for Tagliatelle, Fettuccine and so on, but making larger pasta sizes (like Lasagne) and Ravioli could be hard because this pasta is difficult to work, very elastic, and dries quickly.
So, the usual pasta I use for Ravioli is made with 4 whole eggs each 500 grams (17.8 oz) white wheat flour, salt, and the necessary water (I never measure it, but suppose it's about 1/2 teacup). The less eggs and the more water you use, easier to work will be the pasta...with the practice, you can find your favourite doses according to your taste and to the time you have!
I don't know where to start with recipes...there are MILLIONS of vegetarian fresh pasta recipes! :D
Only two or three "funny" suggestions:
When you have a good practice with plain pasta, you can make naturally colored (and flavored) pasta:
1)RED: instead of water, add concentrated tomato puree or extract (3-4 tbsp each 500 grams flour);
2)GREEN: add spinach puree (boil spinach and process in a blender)
3)ORANGE: add carrot puree;
4)YELLOW: Add a pinch of saffron to the water;
5)BLACK: it's made with Sepia black, don't know if you can find it but black pasta is very nice with seafood sauces!
Another suggestion for a nice presentation of freshly made Lasagne and other flat pasta types: roll the pasta, scatter on the surface fresh parsley or basil leaves, fold it up and roll again. You'll see the leaves through the pasta, with a nice decorative effect.
The first times you make homemade pasta it can be boring and time consuming, but when you have a good practice and can start to play with it, it's a lot of fun!:)