Mick it all depends what you've got. If you've got an RT1 and you prepare it properly you will end up with a pretty decent pre 70 class bike. As Vandy said you will need to modify the frame by lowering the engine cradle 1"-2". If you are prepared to do that, you might as well lengthen the swingarm 1 1/2 ", preferably to a stronger early DT1 rectangular section swing arm. I can advise you off the forum if you're fair dinkum about these mods as it's a bit involved to relate here .
The RT1 engine is one of the more under rated engines in motocross history. It was equally as powerful and efficient as any of the pukka euro open class engines of the day but was overlooked as a serious mount because of the ordinary chassis it came in. The clutch and transmission are as good as anything else but you'd need to look for wear in selector fork and gear dogs as the engine is forty years old and will undoubtably need at least a looking at. If you want to race in pre 70 which is the RT1s spiritual homebase, you'll need an early piston port barrel as the later reed RT2 barrels are not accepted for the class. They respond well to a later model 32mm Mikuni using a TM Suzuki rubber manifold and there are plenty of pipes, both period up pipes like GYT, Bassani or Hooker available on eBay or you could get a more modern pipe like something from GMC or Lozzas Institute. You could opt for up market PVL ignition or if you're on a budget you could use later DT400 CDI which has an external flywheel rotor similar in weight to the original RT1 points unit, or you could use internal rotor MX250/360 CDI. The close ratio DT2MX or YZ250 A gearbox goes straight in. I have a YZ250 A trans in my modified DT1 and a DT2 MX version in the RT1 engine I'm building for my Cheney. The stock transmission and ratios are fine though. The stock porting is fairly ordinary but it doesn't take much port work to get them revving a bit harder. Once again, I'd have to look up my specs and advise you offline. The engine responds to some head work and the reshaping of the combustion chamber or you can use a Webco head or an ACK like I'm using. Unfortunately these things are going through a price spurt at the moment and it's hard to find one for under $300. The stock wheels are extremely heavy and I used an MX250 back wheel on mine (still heavy but lighter than stock) and I use an OSSA Stilleto front wheel purely because it fitted to OSSA Betor forks I use. The best class legal wheels to use are CZ or rare as shit Rickman like I'm using on my RT1/Cheney. For a budget I'd use the stock front brake with an alloy rim and the MX250 back wheel because it looks like the RT1 unit but is much lighter.
The MX360 is a good bike as it comes. I wouldn't touch it too much other than fitting a more modern tapered header pipe PVL ignition and a decent set of new generation reeds. I'd fit a set of YSS shocks and fork emulators to either bike.
These old Yamahas are good old bikes that will give you years of trouble free racing. The reliability factor does decrease the more you modify them (or any bike) so if you want trouble free motoring, keep the mods down to a minimum, limiting them to better ignition, carburetion and exhaust.
Below is my DT1 that has all of the chassis mods I describe. The frame has the lowered engine cradle but I took it one step further and grafted an Ossa Stilletto front frame section which gave me a steeper steering angle and tapered timken bearing steering head. Unless you are posessed by the devil, there is no sane reason to do this yourself. 
