The shrine economy can be very valuable if you use the right civics. If you have multiple shrines in the capital, bureaucracy can really pay off in a big way. I wouldn't go for more than three, however - You start getting diminishing returns fairly rapidly.
The main thing is that spreading the religion allows you to offset (with bureaucracy) 3 gold/turn maintenance per city with two shrines in the capital and the religions present in each of your cities. Because this income is independent from your research/economy/culture slider, you can set research as high as possible even in a large empire, with less worry about maintenance. With banks, et al, it gets even better. This is ignoring the income from other civilizations the religions spread to.
Optimally, I'd run Asoka, Isabella or Saladin. Asoka is the best choice IMO, since organized lends itself very well to this sort of large empire strategy. With halved maintenance costs, each new city may even start out making you more money from shrines than it costs in maintenance. (of course you keep missionaries on hand to convert them from day 1)
Isabella has expansive, but the reason to choose her is that she starts with fishing. If you start near a freshwater lake, that 2 commerce/turn can really help your chances at grabbing the early religions before anyone else. Then use expansive to grow faster. She works well with an early/mid military strategy. Theocracy + vassalage + barracks + citadel = 13 experience catapults. Since they start out at level 4, they qualify for the heroic epic as well. Use the shrines to offset the horribly high civic maintenance costs and go on a rampage. Remember to switch back to organized religion and get rid of vassalage once your units are built in order to get more missionaries to convert cities after conquest (Change civics again when rebuilding the army. Yay spiritual!). As each religious city adds to your income, you can use the freed-up commerce for research or culture to counter war-weariness.
Saladin has philosophical. This means more great prophets, earlier. You can set up those shrines much faster or use them for a tech advantage. He works well if you plan for a cultural victory, but you must remember to set up your second city to produce ONLY great artists. Make a city near lots of grassland/flood-plains, build only farms, mines on hills, use excess food to support artists. Your capital will have so many great prophet points from religious wonders/shrines that getting an artist from there will be an exercise in futility.