Just to say you should really have no problem. There is no reason to spend extra for same day service unless of course you are leaving tomorrow. Once you have everything that is needed you should be ok. If you can get to a consulate get assurance everything is complete before you leave. If you can't, use a visa service and get confirmation from them. Otherwise
www.gotorussia.com is a fabulous website. We got our invitation letters from them rather than our hotel. It's very useful if you are going to 2 or more cities.
You'll have a wonderful trip!!