It's very difficult to predict where your scaling bottlenecks will be. If you're missing a database index for example, queries might run slow, and load balancing your web server won't help.
To start with, you should get comfortable with profiling your application. There's a lot of great tools for the backend, including the Visual Studio Profiler, ANTS Profiler and my favorite, dotTrace.
Next (or maybe first, it doesn't matter), you'll want to profile the client side. Chrome Developer Tools works great, or you can use the new Firefox Developer. This will show you response times and how long it's taking to load assets, like your CSS/Javascript/Images/etc.
After doing both, you should have a good idea where your problem is. But in general, the "easiest" way to improve scaling is:
- Bundle/minify/compress your asset files. You can remove hundreds of KB from page loads.
- Use a CDN. Browsers are limited by domain in the number of simultaneous connections they can make to fetch assets. With a CDN, you can split the requests between domains, and for popular libraries like jQuery, they're more likely to already be cached.
- Cache data as appropriate. If there's some mostly static content that never changes, cache it instead of querying your database every time. Take advantage of things like Output Caching, where your entire rendered view is cached.
- Check out some of the checklist items in this post.
Once you've taken all those steps, if you still have problems, then you can look at things like load balancing and better hardware. Otherwise, you risk throwing money away when it might not make a difference at all.