Before you go lining the lawyers pockets make sure you have a reasonably solid idea of what you want to do - it's all a bit academic otherwise. Think carefully about how you are going to monetise your idea - where does the revenue come from? Have a really clear view of your potential customer and what they might want and pay for. Have a reasonably clear view of whether you can get something to market without startup money. The later you leave it to get money the more of your own company you will own and the richer you will eventually be.
Talk to startup people in your local community. Not only is it a great way to meet like-minded techies, but it will make you a great network if and when you do finally need to find resources to execute on your master-plan. In general you are likely to find them a pretty open-minded and accommodating bunch. Don't feel you have to tell them your secrets, but ask them about how they got started. They will probably be a route into the local Angel or VC network too.
If you are not directly competitive with your current company then they are likely not to be interested in pursuing you for any IP you may create. In general the clause in your contract is to protect them from employees running off with the ideas and setting up shop in direct competition. Contrary to popular belief most big corporates are not really interested in owning your hobbies. Plus they only very rarely take up the option and most courts would probably kick it out anyway.
Last of all, stay in the day job until you either can't face it anymore and are willing to step off the edge of the world, or you can see where your first pay cheque is comeing from in your own business. Anything else is very risky - not completely silly, but very risky.