I play Monarch/Epic with Solver patch (improves AI) with Raging Barbs, Random personalities and 2 extra AI civs, so I rarely have the chance to get an early religion as I need to get archery and either Horses or Bronze hooked up fairly early. You don't need a religion to win, but a good one to get is either Code of Laws (which you need for courthouses) or Philosophy (which you lightbulb from a Great Scientist once you have all of alphabet, code of laws, math and meditation; you might have to build the Ankor Wat to get the Great Prophet though). While the income from a shrine is nice, if you build enough cottages and run enough scientists, you can keep your tech rate up.
I find the early religious techs don't help much if you don't get the religion. The key early techs for keeping your research up are Pottery & Writing for cottages (especially riverside or on a flood plain) and scientists. Sailing helps more for Financial civs but in any case you need to get your commerce from somewhere. Monarchy is the key tech at the end of the early religious techs as it allows your cities to grow much larger. Currency and Code of Laws are other key techs. However, you must play the map. If you have jungles, then iron, sailing, math and then calendar become more important. (I disagree with the one of above poster re plantations - you can trade the resource to the AI for more plus you get the commerce right away) If you have a lot of coastal cities, sailing and and masonry are of greater value if you want the Great Lighthouse) or Metal Casting (for Colossus if you have Bronze) and Trireme's to protect your fish. If you have lots of wine, you lean towards monarchy.
Wonders can be addicting, but they cost a lot. Unless you are Industrious or have the 50% resource coupon (cost is often halved if you have a certain resource), so you should think very carefully whether you need them. Maybe building a library, courthouse, a worker for the new city you will found and a few more troops to keep the AI Civs/Barbarians off your back will help you better.
If I was to offer 2 pieces of advice, I would say (a) more cottages/specialists and (b) play the map and to a certain extent your leader as well.