I've been to Rome 4 times and 3 of them were in October/November. One year it was very cold and sunny, the other 2 years it was mild and warm. Bring a hoodie/jacket you can layer and maybe a short sleeved t-shirt or two. That should cover just about anything temperature-wise. It was dry most of the time but I always bring a small, compact umbrella just in case.
Rome is an easy city to get around. The historic area is quite compact and easily walked. Unless you plan on being out in the wee hours of the night- any area you stay will be perfectly safe. Take the same precautions you would in any cosmopolitan city.
I like
www.venere.com to look for hotels in Italy. I have used them 4 times and have never had any problems. I opt for something small and inexpensive as I end up spending most of my time out exploring and use my room only to shower and sleep. As the other poster mentioned hostels are an affordable option.
Have fun in my favorite city.
