It really depends if you can finance your new home without selling your current home. Do you want to retain 2 homes and turn one into an investment rental property ?
It is ultimately going to depend on your financial situation and your real estate goals. If you are in the position to keep your current property and use it as an investment property and purchase the new one, then that is always an option. If you need to sell your current home before you buy a new home, you will be purchasing "with a contingency". Which essentially means you are saying you will buy the new home, contingent on your old home selling.
My best advice would be to find a trusted real estate agent in the area that can walk you through this process, and find a trusted mortgage lender that can look at your financial situation and give you advice on the best route to achieve your real estate goals. Good luck on the process!
If you are hoping to buy a house, you likely have a budget in mind. Hopefully, that budget includes fees that come with the process, not just the purchase price. The good news for buyers is that they aren't directly responsible for paying their agent. Agent fees usually fall on the seller.