I did Orizaba solo in May. I agree on coments made so far. You definitely don't need guides on Orizaba. The approch from Tlachachuca via Piedra Grande is so obvious if you have experience you claim, it will be a very pleasant walkup for you but don't forget climatization. There are hundreds of Mexicans and Gringos trodding up the mountain. The path is so obvious through the gully to the glacier and then you see the rim all the time. All you need to do is traverse the glacier west until you see the summit and then push for the summit. Graet glissade on the way back.
Don't bother with the car, unless you have driven in Mexico before. Public transport is excellent and reliable there and between Puebla and Mexico City luxuirious and cheap and frequent. You must have a truck to get to TH. The road from Villa Hildago to Piedra grande is 4WD, and unmarked, so don't even try to get there by sedan.
My advise is to fly to Puebla (Continental from Houston), stay in Puebla one night, catch the bus to La Malinche, climb the peak with 1000 people on a path to the top. Catch Bus back to Puebla and catch the bus to Tlachachuca. In Tlachchuca I recommend to stay in Hotel Gerard in clean and private room rather then in a stable of senior Rayes with many other people, especially if you speak Spanish. Senior Gerard charges $15 per room and gets you on the mountain and back for $100. His place and service is very cool, he has a climbers register and it is cool to read it. Bus from Puebla costs $5 (2hrs ride). Puebla to La Malinch $4. Hotel in Puebla $20-40. Food in Puebla excellent and cheap and in Tlachachuca cheap but very simple. I can e-mail you my trip report, if you want to, firstname.lastname@example.org, and anver you questions if you have any.
The gear: sun glasses and sunblock,iceax, crampons, stove to cook food in Piedra Grande in Refugo, you get fuel from the hotel, take food from USA, bottled water from Tlachchuca, sleeping bag, map is not required unless you one of those people, who need map to climb mt Si.
mexico is very nice. I recommend to see piramids near Mexico City or Choala pyramid near Puebla if you have time, it is a day trip from Puebla and you can get there all the way on the bus. Have a great trip