I actually tried it myself a few times these last days. So I'm writing down my experiences and perhaps they will help you if you want to give Rome another attempt.
The start is pretty random.
Sometimes you are at war with either Carthage, Greece, Egypt, or even all of them. If you start at war with Carthage, don't leave your galleys outside of cities within range of their Trireme.
Carthage usually has 3 archers in their capital. If you wait a few turns, it will grow to size 2 and you can capture the city instead of razing it. You can often also capture 2-3 workers from them before or when taking their 2nd city.
It is true that the amphibious attack with no casualties isn't guaranteed.
If you don't mind, you can save and reload and attack one, two or several turns later. This will usually produce a different combat result. I think most of the time you will lose 1 out of 4 attacking units.
If you don't want to reload, you would need to produce more units first before attacking.
If you don't want do the amphibious attack, you will very likely lose at least one Galley to the Tireme they have parked in the city. Perhaps, to avoid this, one could try to offload the troops near their border before declaring war?
I kept Carthago and razed their 2nd city (usually 2W of Carthago). I guess you could also keep that 2nd city (needed for 2nd UHV anyways) and use it to produce some units. (more resources now vs. "better" city placement in the long run).
But I prefer building a 2nd city without BFC overlap later.
Greece sometimes has only Warriors in their cities. Other times they may have Archers and/or Phalanx units.
It's also random which city's are founded by Greece. Sometimes they may even settle a city in Italy which will then flip to you.
Either way, if you drop your Praetorians on a hill next to Athens, you can usually take it on the next turn with minimal casualties. Any remaining Greek cities are usually a pushover.
Sometimes you can capture 2 or 3 workers from Greece as well. But I had a few attempts where they didn't have a single worker somehow.
I usually keep Athenae and Constantinopolis.
I like to build Salonae 1N of copper soonish, as that spot has almost no overlap with the other greek cities and anything north of that will flip to Germany (check Spawns: Medieval civs :
http://rhye.civfanatics.net/civ4/rfc-atlas.htm ).
Of course if Greece builds some other city in that area, you could also keep it (more resources now vs. "better" city placement in the long run)
Tech
Tech trading with Egypt was possible pretty reliably for me. Sometimes you have to gift them a cheap tech first to raise their opinion. Pretty sure that you don't get techs for nothing in RFC, but it's no problem to do "unfavorable" trades, because the AI will usually lag behind anyways and I think they can't trade your techs with other civs, right?
On some occasions it was possible to trade some techs with Greece, Babylon or Persia when they spawn.
Research: I went for mathematics + construction asap, for the 1st UHV and to build the Great Wall.
Currency (+1 Trade Routes) CoL (Courthouse), Compass (Lighthouse) after that.
Research is likely to tank the more cities you found / capture. (I believe anything beyond 10 cities gives you penalties and increases the costs for techs).
But still, you are probably the uncontested Tech Leader at that point and until Arabian and European Civs spawn with a few techs which you don't have yet.
Happiness:
You can get Silver quickly by founding a city in Spain. (When it flips to Spain later, you should have enough from other sources)
Sometimes you can trade for Monarchy pretty quickly, which is a huge boon (unit happiness + Whine)
At some point Egypt may want to become your vassal, which gives you trade access to their resources (Gold / Ivory / Cotton).
Early cities:
3 in Italy:
Rome on the spot.
Mediolanum (flips on turn 3?).
And I suggest Pompeii, on the hill SE of the pig. It can work the Pig, Sheep and two Mines to get some production quickly. And grow on Clam and coastal tiles later. Its also useful for early galley movement.
You then have one more settler.
I think its convenient to transport one settler / archer via galley to Spain, 1N of the Silver, right at the start. Build a worker there and hook up the Silver asap. The archer can try to walk towards the goodie hut at the west coast.
Another possibility is to found Lugdunum to work the horse and build some units right away. (But that city is automatically founded later if you don't).
Carthago can be caputured and won't flip away later.
Athenae the same.
Greece often builds Constantinopolis.
1st UHV (turn 154):
These cities should have enough Food / Production to build / whip the required buildings (5 Barracks / 5 Aqueducts / 5 Amphitheatres) for the first UHV goal, as well as some Units and Wonders.
(If you try to save the game, the filename will tell you which turn you are in. So you know how many turns remain to construct these buildings.)
Units:
Europe:
Celts will start to roam in France, Spain, Germany at some point and will usually threaten your cities.
A single archer per city is probably not enough, and if you want to reliably deal with them, you might need some units (1 or 2 Axemen) to defend Mediolanum against roaming Celts.
At some later point, lots of Barbarians will spawn pretty much everywhere around you. Either you have the Great Wall at that point, or you need many more units.
Africa :
The Great Wall, if built in Europe, doesn't protect these cities.
You need to deal with Horse Archers (Str: 6), Impis (Str: 4) and Camels (Str: 10). I would say two Spearmen per city are pretty much mandatory at some point.
The Mediterranean:
Barbarian Triremes will spawn from time to time in the Mediterranean, so you need 1-2 Triremes of your own if you don't want your Resources pillaged by them.
City requirements for the 2nd UHV:
You can check the specific tiles for these regions at the RFC Atlas.
Click the checkbox at UHV Areas: Rome:
http://rhye.civfanatics.net/civ4/rfc-atlas.htm
- 2 In Africa.
Either capture or found yourself.
I like to capture Carthago for the first city.
And later found Rusadir (1NE of whine, 1N of horse, 2E of sheep).
You get to keep these cities.
- 3 Cities in France
They spawn automatically if you have no units nearby. And you also need 3 for the UHV, very convenient.
Lugdunum
Burdigala
Lutetia Parisiorum
These cities will flip to France at some point.
- 2 in Spain.
You need to found these yourself
These cities will flip to France at some point.
- 1 in England.
You need a galley NW of France. There usually is a celtic galley there at some point.
I don't think there is enough time to make this city worth it, so I suggest founding it as late as possible.
That city will flip to England at some point.
Early Wonders:
One start, I was even able to build The Oracle in Rome, but usually that Wonder is already built or will be a few turns after your start.
In my games the Chinese often have the Hanging Gardens already built at the start.
The Pyramids is pretty much a lost cause, either already built or finished a few turns in.
Temple of Artemis: Sometimes available.
Moai: Often available. Nice to have in Rome or another city, but not essential.
Great Lighthouse: I was reliably able to build it in Pompeii by working on it from the start, and improving the Pig right away with the two starting workers, without doing other improvements in that city.
The Colossus was often available as well.
Mausoleum was often built in India / China.
Colosseum is often build in China before I get the chance.
The Great Wall: Very helpful to have.
With enough luck and/or science lead, you can build / chop most wonders after that.
3rd UHV
If you have the Great Wall in Europe, then just make sure to get some Units to protect the two African Cities, and it's pretty much an automatic win.
If you are unlucky, you might experience stability issues due to your cities joining Spain / France / England, but I don't think that is a problem for the completion of the UHV.