Bumper plates are to pricey right now. So if I build a platform with rubber and wood would dropping the "standard" plates from overhead and shoulder height damage them or just be loud?
It would not be good for the plates and, especially, the bar. If you had sand pits on either side or thick cushions, it would likely be fine, but a platform of rubber and wood is too hard.
Build your platform, but hold off on dropping weights until you can afford some bumpers. Glenn Pendlay has some good deals on his Wichita Falls Weightlifting site.
They're both pretty important in maintaining the longevity of your equipment, but I would probably prioritize the platform.
Build the platform first but keep in mind that dropping iron plates from overhead will do very quick damage to your bar.
Check IronWoodyFitness.com for bumper plates. They are fairly affordable for the bumper plates of different sizes (not competition plates). You may be able to find them cheaper from other sources as well. But I use and recommend Iron Woody equipment.
I bought a bumper set and bar from Wichita Falls Weightlifting. It was one of the best things I have ever done.