There's a lot of information already posted on this forum, but we do need more organization! Case in point, we don't yet have a master thread and sticky for Rome dining options. In any case, with FT it's always advised to first do a search on what you're after. To help get you started these threads will prove useful:
Please recommend your favorite non touristy, non super fine dining place in Rome!
Food in Rome
Some good resources for determining where to eat in Rome
And of course this very recent thread:
1st time eating in Rome
In that last one Pastificio is mentioned. Here are two articles on it, one from Amanda Ruggeri's Revealed Rome and one from Elizabeth Minchilli:
Pasta for 4 Euros? Yes, Please
cheap eats in rome {pastificio}
Here's a relevant post from Katie Parla:
Budget Dining in Rome, 2017 Edition
And from Natalie Kennedy's [recently discussed] blog:
7 Best Places to Eat in Rome for Seriously Cheap
Happy researching!