The Oblivion Gates don't start randomly spawning until after you rescue a certain person from a certain city. Giving the amulet to Jauffre will not have them start spawning.
This is true. Giving the amulet to Jauffre won't start spawning gates, but what happens a little after this will.
Thanks to Oblivion's levelling system (unless you're using OOO or FCOM) and its monster scaling system, doing the main quest earlier makes it really easy.
Thought I'd clarify for the OP that OOO and FCOM are mods that change the levelling system. In the vanilla game, as Xzalander said, doing the main quest earlier is easier because at later levels, you'll encounter tougher enemies, and find yourself having your backside handed to you.
The levelling system in Oblivion is opposite to Skyrim- in Skyrim you get stronger as you get to higher levels and choose more perks, but in Oblivion, enemies level with you. This means when doing the main quest at Level 20+, you'll be fighting http://www.uesp.net/wiki/File:OB-creature-Xivilai.jpg instead of http://www.uesp.net/wiki/File:OB-creature-Stunted_Scamp.jpg that you'd encounter in the early levels.
A lot of players here never bother doing the main quest at all (or only doing it once, with one character.) But if you definitely want to do the main quest, my advice would be to do it now before you get too high in level, because tougher enemies mean it can get really frustrating.