The immediate step after your offer is accepted is to complete any inspections you elected as contingencies in your offer. Typically, you will have a 14-17 day window to complete your inspections and negotiate the findings. The standard timelines vary by state and will be negotiated with your offer.
The most common and most highly recommended inspection is a Home Inspection. During this inspection, a certified Home Inspector will scrutinize everything in the home from the foundation to the roof. If any potential issues are found, your inspector may recommend additional inspections by a specific professional- plumber, electrician, roofer, etc.
Other common inspections to consider when buying a home include a radon test, pest inspection (these two are highly recommended and can often be completed by the same company and at the same time as your home inspection), a sewer line scope, chimney inspection, septic system inspection, and structural inspection. The location of the property and the condition of the home should indicate which of the inspections are necessary. This may sound a bit overwhelming but luckily, I know all the best inspectors around and will guide you every step of the way!