Follow these steps to purchase your first home in a new city:

1. Determine your budget and savings: Before starting the relocation process, it is important to determine your budget and savings that can be put towards buying a new home. This will give you an idea of the price range for homes to consider and the amount of mortgage you may qualify for.
2.  Research the housing market: Conduct research on the housing market in the area you plan to relocate to. This will give you an idea of the average home prices, desirable neighborhoods, and any potential red flags to look out for.
3.  Find a reliable real estate agent: A real estate agent can be a valuable resource in helping you find and purchase your first home. Look for an agent with experience in the area you are relocating to and who comes recommended by friends or family.
4. Plan a trip to the new city: If possible, plan a trip to the new city to scout out potential neighborhoods and homes. This will give you a better sense of the area and help you determine the best fit for your needs.
5. Get pre-approved for a mortgage: It is important to get pre-approved for a mortgage before making any offers on a home. This will show sellers that you are a serious buyer and help you know what price range to stick to.
6. Make an offer: Once you have found a home that meets your needs and budget, work with your real estate agent to make an offer. They will help you negotiate the best price and terms for the home.
7. Have the home inspected: Before finalizing the purchase, be sure to have the home inspected by a professional to identify any potential issues or repairs that may need to be addressed.
8. Coordinate the moving process: As you get closer to closing on your new home, start planning and coordinating the moving process. This may include hiring a moving company, packing up your belongings, and arranging for utilities to be turned on in your new home.
9. Close on the home: Once all the necessary steps have been completed, you will close on the home with the help of your real estate agent and lender. This will involve signing paperwork and paying closing costs.
10. Move in and settle into your new home: Once the keys are in your hand, it's time to move in and start settling into your new home. You may need to make some additional trips to the new city to tie up loose ends, but you can now enjoy your new home and community.