Congrats on the new car. You've not told us anything to help you, like mileage, transmission type, and did you get any service history. Also, what is your DIY competency level and what facilities and tool kit do you have. If you plan on keeping the car for a long time, my tips are these:
Whatever the used car lot seller told you, don't believe them.
Buy a BMW scan tool of your choice and scan the car for trouble codes.
Baseline all the fluids by changing all the driveline fluids - engine oil, engine coolant, transmission oil, and differential oil. Use BMW LL-01 spec engine oil and an original equipment engine oil filter which is a MANN HU-816x. The engine does not need 3,000 or 5,000 mile oil changes. It easily can handle 10,000 mile oil changes IF the oil service is done correctly. Most owners are scared to go over 7,500 mile OCI and settle at 7,500 miles per oil change. But the N52 does well with higher intervals.
Flush and fill the brake system fluid and clutch circuit if it is a manual transmission car.
Educate yourself on the Condition Based Service (CBS) system. It is a helpful tool to use for service requirements. And please read this:
www.e90post.com/forums/showthread.php?t=1533444
Inspect the OFHG, oil pan gasket, and the valve cover gasket for leaks. Clean and swap the VANOS solenoids. DIYs are on E90 post for all of them in the DIY section.
Inspect the thermostat hose that leads to the cylinderhead. If it has a black plastic hose bibb, consider swapping to the aluminum hose bib. Google "N52 Mickey Mouse flange" for info.
This site has been up for 20 years. EVERY question you will have has been answered multiple times, if not hundreds of times. Search for answers and read the forum. Posting a "I just Bought a BMW, What should I do" thread is a little annoying TBH. All the answers are here already. Just friendly advice. We can help if you don't understand something after you've searched for the answer but don't understand the answer; we can offer clarification.
You have an old BMW, it will last a very long time and serve you to very high miles if you take care of it and service it properly and CORRECTLY. Save your funds for upkeep and maintenance. You do not need to over-service the E90, it will not make the car last longer or drive better, or breakdown less. Buying a muffler for it is a waste of money. Keep the car stock and it will not give you troubles. Use BMW parts.
Lastly, if you are not going to DIY, then find an Independent BMW specialist and tell him what your plans are for the car. Meaning, tell him how you plan to use it, how long you plan to keep it, and how many miles you want to get out of it. This develops a good relationship with your mechanic so he can service your car effectively and efficiently. It is not good to take a BMW to a random shop and ask them to fix it because you will get played for the most part. If you are going to use a mechanic, then use E90 Post to educate yourself on your so you can speak intelligently with your mechanic regarding your BMW's service needs and repairs when required.