I'd stay away from the convertible approach as it now creates different motivations for the founders - especially if things get tough (and they typically do). The 2 investors may make decisions more motivated to benefit the Series A shareholders while investor 3 will always be more focused on the outcome for common. Even if this doesn't really manifest in decisions, it'll be in everyone's minds and be a source of conflict at exactly the time when the 3 of them need to work together.
Also, it's a slight exaggeration, but a convertible note essentially means 2 founders are just *giving* the company money in most scenarios. It's not likely a large amount of money and it'll convert to a very small amount shares relative to their founders' shares. Yes, there's a liquidation sweet spot (e.g., <= 1X Series A size) where founders would get some of their money back, but statistically it's not likely. Kind of a crap deal for the 2.
A straight note at least has some potential of being paid back... and investors may not grimace if it's negotiated to be paid back at some future time when cash flow allows... or it could simply be negotiated into converting at Series A. In any case, this provides founders most flexibility and doesn't instantly create two tiers of founders.
Depending upon amount of money, another possibility is to improve optics by having the employees paying for some of the expenses directly and then simply file expense forms... it'll now sit on the balance sheet as a payable, not as debt. Psychologically, investors are less fussed about paying back bills than they are paying off debt.
I guess a final approach would that the three amigos all do the same thing (whatever it is) but have the company lend amigo 3 the money.