I spent several days solo in Bangkok before a tour elsewhere in SE Asia. It's a huge, sprawling, noisy city - with unbelievable traffic! However, I had traveled to other large Asian cities (Beijing, Hong Kong, Singapore, Seoul), so it was not that much of a shock to me. The people were great, the food was terrific, and the sights like nothing you've seen in Europe.
The Skytrain (subway/train) was easy to navigate and I took it several times on my own. If you have taken a subway in any other large city, you will be able to figure this out. There are boats on the river that act like bus routes. This is also a great way to travel through the city (and you get some views too). I've heard that some of the hotels along the river have their own shuttle boats that will take you to various places. I did not travel by tuk-tuk, although a lot of tourists do this. To me, it didn't look like that much fun in the heat and traffic (and it will be HOT!)
I stayed at the Evergreen Laurel Hotel Bangkok on Sathorn Road. It is not on the river, but very close to a Skytrain stop that will quickly take you to the river or wherever. I believe this 5-star (or 4-star, not really sure) hotel is owned by a Chinese or Taiwanese company, so many of the guests were Asian, but the staff had good English and were very helpful. (This is another reason to stay at a good hotel. The staff can help you figure out public transportation, get a cab, exchange money, and answer the many, many questions you will have.) The room was large, comfortable, clean, and the breakfast was fine. I looked online, and their rates seemed to be around $70-$100 right now. Once you get away from the really glitzy hotels on the river, I think you can find very reasonable rates.
I hired a private guide for one day from Your Thai Guide, https://yourthaiguide.com/ They organize a tour to your specifications. The guide picked me up from my hotel, we took the Skytrain and cabs to the various locations, we saw many of the major sights organized in an efficient way, we took a boat ride off the main river, and had a delicious lunch.
I also took a food tour from Taste of Thailand food tours, https://www.tasteofthailand.org/ We met near a Skytrain station mid-morning and went to six or eight places for tastes of food. The group was small - maybe seven or eight people. It was a great way to try some out-of-the-way locations that would be hard for a tourist to find, and the food was delicious.
Many tour companies offer transfers from the airport. I arranged a transfer from Oriental Escape, https://www.orientalescape.com/ It is true that you can take a cab, or even the train, from the airport. But after the really long-haul flight, it was nice to see someone with my name on a sign to get through the very busy airport transportation hub and straight to my hotel.
As I said above, the weather will be really hot and humid. I found that the best way to deal with this was to get out sightseeing in the morning, then return to the lovely air-conditioned hotel mid-afternoon for a rest, and then go out again in the evening when the sun was low/gone.
This will be quite an experience for you! Have fun.