The situation is not exactly clear to me from your description, It sounds like you have an interested first time investor and he is a soft-commit for a considerable amount. You are looking to raise $500K, and you have a Term Sheet that you have prepared, but it has not been negotiated with any lead investor. Since this investor is a first time investor, he may not be very well qualified to be the lead and do the due diligence. Does your Term Sheet have a minimum amount that must be raised for the deal to commence? For instance, the target might be $500K, and no money will be taken unless you reach a minimum of $300K. In that case, if the investor intends to provide, for example, $100K, he could sign the Term Sheet and write a check and you would return the check if you never got to $300K. This would turn him into a hard commitment. Of course, once you get a more seasoned investor, you may end up needing to negotiate the Terms, which may require modifying the Term Sheet and having that original investor sign a new one. This probably wouldn't be a problem, since the Terms would probably have gotten better for the investor. Really though, the thing you need is the lead investor that will go ahead and do the due diligence and commit to some level of funding, even if that is small. You have a big head-start with the other investor. So, take the introductions and find that seasoned investor that is willing to be the lead. Hope that helps.
There are no "hard and fast" rules here, so it is no wonder that exactly how to do this is not clear. Typically, a "lead investor" performs two roles, both leading to increased confidence for "followers". First, the lead commits to signficant funding, maybe 25% of the round. Although this percentage is highly variable, the idea is that the lead commits in a signficant way. Second, the lead does due diligence and negotiates the Term Sheet. The lead would typically do things like make sure your books are in order, make sure you have signed non-competes, etc. with employees and any contractors, etc., etc., etc...the due diligence. The lead also negotiates things like the liquidation preference, the valuation, etc. and hopefully can speak to why the deal makes sense with the given Term Sheet.
You initial investor sounds like he fits the first of these and perhaps not the second. That's ok. Several things could happen here. Sometimes deals come together without any lead performing that second role. The founder (you) puts together the terms and manages to rally investors around the deal. This can be challenging though. Some investors want to be followers and want to have an investor they trust that has done the due diligence before they invest. Also, if they question the terms, you don't have any investor on your side that can argue that Terms make sense as they are.
So, ideally you want someone to do the due diligence and get that out of the way. Since you've got this one person providing the initial investment, it is much less important that the "lead" doing the due diligence put as much money in. I could see the possibility of essentially having two people split the two roles that one "typical" lead performs. Remember, no hard and fast rules, so "typical" doesn't mean too much.
If you are comfortable that you could execute on the business plan with $250K, but ideally you want $500K, then you could also modify the Term Sheet to require a minimum of $250K before a first closing. Then you could have the initial investor go ahead and sign and write the check, which you would hold until you had a minimum of $250.