The best places to buy shoes and clothes are the "bancarelle" (stalls). They can be found everywhere in Rome but the most famous ones are those in Porta Portese, a flea market in Trastevere. Porta Portese is open every Sunday and you can find just about anything there at very low prices. Be sure to get there early to avoid the crows...and watch out for pick-pockets!
Other popular stalls are the ones at the Ottaviano metro station. Thursday is the best day to go there. On Via Ottaviano itself you'll find lots of shops at affordable prices. The market at San Giovanni is the oldest and biggest market, it's near the Basilica di San Giovanni. Another great area for bancarelle, is Viale America, near the Eur Fermi metro stop. You will surely find bargains there, prices are very low because it's not a very touristy area.
If you're looking for fruits and vegetables, go to the Testaccio market, not far from the Piramide metro station. Very good quality fresh fruits, vegetables, fish, meat, and bread at good prices. The markets at Campo de' Fiori and the one in San Cosimato are rather expensive since they are visited by many tourists.
The best way to save on food is to go to the big supermarkets in the shopping malls (Panorama at Granai in the EUR area of Rome is a very good one). The new shopping mall EUROMA2 also has a great supermarket. If you can't get to the malls, go to local supermarkets such as TODIS, DESPAR, SMA, BILLA, PAM etc. They often have discounts and special offers such as 3X2 (buy two and get one free).
As for WATER just fill your bottles at the many fountains found all over Rome!!!
If you want to eat out, avoid the tourist places, go where the local people eat. Moreover, most bars now have a "tavola calda" (hot food section) where you can eat full meals at reasonable prices.
Here I am at the EUROMA2 shopping mall.
I'll be posting more tips and advice later.