Inviting Jesus into your heart really does work. I've known a lot of Christians who attest to it.
But I think you have to be sincere, and really want it, not to prove to yourself that spirituality is real or that you're really "spiritual" (whatever that means
).
I myself didn't go through Christianity, but through Advaita Vedanta and nonduality. This is actually where being an analytical thinker and having good discrimination is a great advantage. Check out
Franklin Merrell-Wolff who was not only a mystic but also a philosopher. Check out his book (partial)
here, it is really good
The sages of Advaita Vedanta also layed out a systematic philosophy of Self-Realization that can be very useful for the spiritual search. Here are some good websites:
Shankaracharya Nisargadatta Maharaj Ramana Maharshi
A very easy way to have a spiritual experience or awakening is to visit spiritual teachers in retreats or satsang. They transmit a tangible energy field / aura that is conducive to higher spiritual states and awakenings when you are there. That aura is also reachable through books and tapes but is most powerful in person. Meeting teachers in person is perhaps the best, easiest, fastest, and most powerful way to speed up your spiritual path, especially if you haven't had an awakening yet. After you've had an awakening you can meditate at home and progress, but if you don't even know what Truth is yet, you should go meet as many teachers as you can and stay in their energy field as long as possible.