Congratulations on your new bike purchase. I had a 2000, 2002, 2003 YZ250, they were all great bikes. That 250 two stroke engine is nearly perfect in your bike. In 2003 Yamaha made transmission improvements. They have continued that make small changes in an already best in class bike.
What's your weight, don't tell but if your heavier than 200 then consider using the optional heavier springs for MX or you will suffer. Set your rear sag at 95-100mm so the bike will sit properly in corners and do what it designed to do. I too raced BMX as a kid prior to Motocross racing, it's a great foundation.
I ran Bel-Ray MC1 back in the late 70's and had two failures. The cylinder and crank looked like they were run without lube. I switched to Klotz as mentioned above and had good luck. In 2000 my YZ 250 crank had a lot of wear in a short time so I dropped Klotz and went with Amsoil in the last few bikes. Amsoil Dominator has been extremely good for my bikes at 40:1. What ever you use stick with it as metal doesn't like mixed lubes. Avoid castor based oils, they protect well but gum up power valves and separate at low temps. Yamalube-R at 32:1 has been a good oil for a lot of friends in a lot of brands for over 30 years, it's readily available.
Get an experienced rider to show you how to care for your air filter, that is the most important preventative maintenance you can do. Keep dirt out of your engine!
Radiator fluids at 60 percent water and 40 percent coolant will protect fine and offer better cooling than 50/50. Changing suspension fluids once or twice a year will keep things in check for you. As mentioned by Brothaman keep the transmission fluid changed often. There is no filter and the oil get hot from clutch friction and gets a lot of shear from the gears. Get a magnetic drain plug from your dealer.
I buy oil by the case. I run Amsoil in my car, truck Harley, MX bikes so I use the 10/40 Motorcycle oil in the transmission. I have no history with the Bel-Ray Gear Saver oil and have heard nothing bad from others that use it.
Have fun...