October in Rome can be fabulous, summery weather and 25C temperatures - often one of the nices months of the year and a great time to visit! Extremely heavy winter rains usually start in November, but if you are unlucky, there can also be some heavy rain days in October. So check the weather forecast before your trip.
Italians dress by calendar, not weather. The switch usually happens sometime in October so you may see gilets, light down jackets and merino sweaters and even boots although it can still be really warm. If you wear shorts and sandals, you will stand out. I would wear closed shoes. Fancy high-tops and sneakers are fashionable here. If you are in touristy parts of Rome, you can wear anything, including cowboy boots, a stetson and a fanny pack 
You will just be seen as another species...
Normal Roman streetwear is formal and understated (hence a no to blingy sandals). In my part of town, most men wear suits or very dressy casual outfits. Women are usually stylish and pared down, shades of gray, nudes, navy and brown. Accessories are top notch. Lots of dresses and blouses. Few t-shirts, long-sleeved ones are really rare. Scarves are not very popular here. Italians love denim. This spring I've worn a utility jacket (all younger women seem to have one) with jeans and high-tops.
Be careful with your belongings, pickpocketing is a real issue here.