Hello there ludookia, nice thing you also have a Yamaha Jog there. What country are you from? Here in Manila, Philippines and as well as on the provinces, most scooters are Yamaha Jogs & Honda Dio.
About your Scooter w/c also almost same as mine, you have two options. If you have the budget and you want the maximum power and acceleration, make your engine to 70cc. There are lots of performance parts available for the 70cc kit. You have the option to choose from Malossi, Hebo, Polini, Metrakit and many more. Try to search threads about 70cc tuning here.
And other option is to tune your 50cc engine. As a novice racer, I decided to race with my 50cc jog engine. Here are some of the modifications done on my 50cc bike: CMR Crankshaft (full counterweight), SKF 6204 C.3 Crankshaft High Speed bearings, Koso intake manifold, 24mm OKO carb, Port & Polished (by Tiba) stock cylinder rebored to 42mm & converted to Liquid Cooled Cylinder. I used Seletra ignition previously, but now, i want to experiment on stock magneto, I will try to use the modified stock ignition (Lightened flywheel & on the stator, coils for lights removed except for the primary coil);
Home made Racing CDI, Malossi Variator, Malossi Torque Drive, Malossi Yellow Center Springs & Clutch springs. For most 50cc jog racers here, stock 2-pad
2JA clutch is enough. but if you can, get the delta clutch. I use a locally hand crafted pipe. I have a malossi replica and a straight pipe derived from a
80cc kart pipe. For the suspension, i used the OKO gas filled rear shock. On the front, im still using the stock HD suspension. I used KOSO floating big disk break. Also used the KOSO quick throttle. For the wheels, I changed them with RPM Racing Mags with Dunlop TT91 90/90-10 tyres. With the parts I used on my ride, you will find its really cheaper as much as 1/3 of the price compared to the European brands. But if you have the thick wallet, go for the European brands since they are designed to last longer.
Some pictures of my scootz are on our local MC site
http://motorcyclephilippines.com/photopost/showphoto.php/photo/12281/sort/1/cat/500/page/1. Try to visit our site and you are very much welcomed and your inquiries about jog50s will be much entertained.