The OP mentioned his desire to visit the Appian Way so here's my recent experience (from this past April).

I head read that you should take the bus line 118 and to go on Sundays when the route was closed to traffic. I did alot of research b4 my visit and saw that the 118 runs every hour whereas line 660 runs every 15 minutes or so - and since I hate waiting for buses I took the 660.

Take the metro line A, towards Anagnina. Here's ATAC's map (the map takes awhile to load): http://www.atac.roma.it/files/doc.asp?r=385

I opted to keep things as simple as possible so I chose to take the bus from its originating stop at L.go Colli Albani, (I figured this way I was guaranteed a seat), but you could also take the A Metro one stop further to Arco di Travertino. The 660 bus route goes from L.go Colli Albani ending at Cecilia Metelli.

Here's google's map in street view showing the Cecilia Metelli bus stop at the T intersection of Via Cecilia Metelli and Via Appia Antica. "Virtually" pivot around and you can see the bar/snack shop on the corner where you can get waters, snacks, etc, and where you'll be able to rent bikes if you desire.

Taking the 660 means you'd have to go in one direction to see some sites (and the catacombs) and then back track to see the rest of it, but that didn't bother me. (BTW through Google you can virtually walk alot of it).

Here's Appia Antica's website (I downloaded alot of info from this site and brought it with me as a guide):
http://www.parcoappiaantica.it/en/default.asp

Here's Context Rome's guided tour (it's expensive, I didn't take it) but this website gives a nice snapshot of experiencing the ancient road.

The George Costanza in me makes me share the following ( ) - I found a new, clean, good restroom that I didn't see on the website. It's located in the visitor's center of a new-ish revealed archeology site "Capo Di Bove". Here's google's street view of the entrance. Refer to the street map in the corner of the page that I linked to see where to find it on the Appian Way. You need to go past the excavated area to find the visitor's building with the restroom.

I first ventured to the Regina Viarum (Queen of All Roads) on the suggested Sunday, and found the Capo di Bove installation, but then it started to rain and I hadn't come prepared with an umbrella so I left and returned on a weekday. (I was amazed at how easy it was to get there and back). The day turned out to be one of my most cherished Rome excursions (to date!) Walking southward, there was no traffic, no people - well, an occassional jogger or cycler went by. I actually did see one car come out of the driveway of one of the estates on the Appian Way (can you imagine living there!) but it had to go about 5mph to manage the ancient uneven stones. So in terms of thinking that if you didn't go on a Sunday that you'd be caught up in some kind of freeway environment, think again. The traffic is only bothersome towards the beginning of the road where there's no area for foot traffic, but that's avoided altogether if you take the 660 bus. My experience was fantastic - being that it was filled with views of idyllic Roman umbrella pines and ancient tombstones, possessed that great calming country quiet and all the while my feet trodded the very same basalt stones that the legionaries marched on!!! As an aside, I must say I found it incredibly impressive to think the soldiers marched up and down this road - for me, I had to navigate the stones as if I was crossing a stream, gingerly going from rock to rock (can't imagine the Roman army doing that!) Why it was such an incredible experience for me is that aside from the fact that there were no umbrella pines in ancient times (the pruning started during the Renaissance period) and the tombstones were in a somewhat ruinous state, that what I was seeing, hearing, smelling was very darn near to what was experienced more than 2000 years ago. It's hard to have this same appreciation viewing the remains of Ancient Rome in the city center since you see the 2000 years of succeeding history plainly evident.

Hope this info is of use to someone - I know I got carried away with exclamation marks - but it was enjoyable for me to relive the experience sharing it here.

Edited to add: correction to info on bus line 660. I was checking the links and the 660 does run every 15 minutes on SUNDAY, but the rest of the time it runs every 30 minutes (so this is a reason to go on Sunday if you can).