For simplicity, you might consider taking the bus. Explore this National Express coaches link to learn what your bus options are: https://www.nationalexpress.com/en
You need to know where you are going to arrive at Heathrow and where you need to arrive in Portsmouth. You may need to make a change along the way, but the driver can help you with that.
You can buy your ticket for the bus at Heathrow. There's no need to do that in advance. In fact, it's a better idea to not get it in advance in case the plane is late. Just ask where to go to do that when you arrive and get your luggage.
I did this my last trip to England in 2016, only my destination was Bath. It was much easier than the often recommended bus/train options. And I loved riding on the bus through the countryside and towns along the way.
Note that I did carry-on only, so I can't advise you on the particular details of getting from baggage claim to the bus station. It may be simpler or more complicated for you, depending on how how much luggage you have. I took the shuttle from my arrival location to the bus station. Again, just ask someone how to do that.
The bus station has a huuuge electronic board listing destinations, departure times and bus numbers. The busses are parked outside. It also has a very large and nice bathroom, a coffee shop with food and lots of seating.
Finally, realize that you will be in an English-speaking country with lots of nice people to help you. You don't need to know every detail totally in advance. And no doubt some things will have changed in the 6 years since I was there.
The Central Bus Station images here might be useful.