One thing that seems to be an assumption in a number of replies is that having higher voltage will make the bike go faster; this is not necessarily true, though it certainly can enable higher speeds more easily.
If the motor is wound for a certain voltage, then running it at a higher voltage will spin it faster for the same load on it.
If the motor is a hub motor, then running it at a higher voltage than originally wound for is going to spin the wheel faster, making the bike go faster.
If the motor is wound for a higher voltage (for the same RPM as the other motor wound for a lower voltage) to start with (or rewound to do so) then it will not run any faster, unless you increase it's voltage above design level.
If the motor is not a hub motor, but instead runs thru a reduction gearing setup (as mine does) then while the motor would indeed spin faster, it does not have to make the bike go faster, as it can simply be geared down by changing the ratio of the reduction gearing (as I did when i went from 24V to 36V to increase efficiency and range without doubling the weight of my battery pack).
You could say that the hub motors are "geared" for a certain speed at a certain voltage, and changing the voltage would require changing their "gearing" (windings) to make them stay the same speed at a higher voltage.
All that said, if you intend to use 36V eventually, you might as well start at that voltage. It'll mean everything you get is already designed to work at that voltage, and is less likely to require any kludges or workarounds to get it all to operate together.
Now here's where the math comes in again (I hate math):
Given that you are limited to 200W, @24V it will be drawing 8.4A battery current. That means the battery will only need to be able to supply 8.4A, assuming your controller has an absolute limit on it that prevents higher current draws.
If it is a battery that can output at "1C" meaning at the same level as it's rated Ah, then it only needs to be a 8.4Ah battery to give you enough power to run for an hour of full-throttle use....
...Except that there is an effect (Peukert) that essentially means that the faster you pull power out of a battery, the less power total you can pull out. (also, you can't totally pull all the power out of most batteries, which is called 100% DOD (depth of discharge), without destroying the battery).
It's worst in lead-acid (SLA (UPSs, bikes), AGM (wheelchairs, bikes), FLA (car battery)), but it also affects all the other chemistries to one degree or another, such as Li-Ion, NiCd, NiMH, LiFePO4, etc.
So if you used SLA batteries, you'd probably only get half an hour of runtime, maybe 45 minutes, even at 100% DOD. It's a lot better with other chemistries, but it still affects it.
Now, if you could draw less current, with the same battery, you'd get more runtime, even if you draw the same total amount of power (watt-hours, Wh).
So, @36V it will only be drawing 5.6A battery current. That means the battery will only need to supply 5.6A, and if it's an 8.4Ah battery, then it isn't working nearly as hard, and you'll get more power (Wh) out of it in total. Perhaps a full hour at 100% DOD.
Note that the actual Wh you get out of a battery and actual DOD levels before damage vary with brand and chemistry, but in general it is a good idea not to take more than 80% of the total Wh out of a battery, less if you can help it. It makes them last longer, generally.
All of the above is to show you one more reason why using a higher voltage may make sense. It is one reason i went to a higher voltage.
It's hard to explain in simpler terms (for me, anyway). I'm still a little shaky on some of it myself, mathwise, but I get the basic concepts.
