I concur with Bill Franke and J.R. that you want proposal here. But I don't think it's a matter of formal vs informal usage. It seems to me that the core difference between these two words is the depth of consideration and confidence they imply.
You're in a committee meeting wrestling with a problem and a Bright Idea occurs to you. You throw it out on the table for the group to examine and discuss — that's a suggestion. In fact, if you see dubious expressions on some people's faces you may say exactly that — “Just a suggestion, guys,” to indicate that you're not committed to it, you just think it's worth exploring.
Subsequently, the group looks at your suggestion from many angles, considers its possible side-effects, modifies it in some respects to reduce costs, extends it in other respects to increase benefits, and agrees at last that you're not going to come up with anything better. Now you put all your useful thoughts into formal language, carefully craft your exposition to demonstrate the depth and breadth of your examination, frankly admit possible drawbacks to cover your asses, arbitrarily insert passages (of negligible relevance and dubious legitimacy) which will appeal to management's known prejudices, and pass the document upstairs — that's a proposal. In fact, you may entitle it Framistatitude: a Proposal for Indeflature of Ongoing Porsitility.
Mutatis mutandis, that's how a thesis works. You take a Bright Idea — a suggestion — to your advisor, work it up, modify it, contradict it, revise it, massage it, bolster it with a Review of Literature, rewrite repeatedly; and when you're done you present it to your reviewers. At that point you're committed. You must not offer them anything so tentative and vulnerable as a suggestion: that's an invitation to evisceration. It's got to be bold, assertive, confident. It has to be a proposal.