Yes, you will have performance issues. Every application has database performance issues, even with much smaller databases than yours. You need to study and work to understand how to use the RDBMS technology to its best advantage.
The good news is that you can do it. A database of 4GB is not excessive, and many success stories involve databases that are much larger.
I suggest you start by studying the following resources:
Combining technology like the APC cache or Memcached with PHP and MySQL is also practically required for high-performance PHP applications. Because the fastest database query is the one you don't have to run (because the data is already in a cache).
We can't answer your question about getting query results in 30 to 60 seconds, because we don't know what type of queries you need to run. There are many other factors for performance. The naive and general nature of your questions indicates that you have a lot of study to do before you will be successful.