Hi, Zoomtrain, and welcome to the forum.
A few personal observations:
1. Do NOT buy a set that comes with a WIRED remote control as the one you showed us. I have one and do not like the wired remote at all. It is a cheap piece of plastic that Marklin should not have put on the market. The track piece it attaches to is even worse. Looks like a home-made job.
2. Having said that, very similar sets exist that have a WIRELESS remote control and they are very good. I have two full sets of remote and control track and I love them. So does my grandson (3).
You can also buy one or more wireless remote controller(s) (not expensive) and then you and your kids can each control a train on the layout.
These sets have one issue, though, they automatically shut off after three minutes. You need to have this "feature" (I call it a defect) fixed so that does not happen if it bothers you (it bothered me). There is lots of info on this forum on point.
3. As for buying a set with an MS2, maybe. The MS2 (do NOT confuse it with the old MS or MS1 as it is called) is a fairly complicated controller to use, at least for me. Unless you are certain you will go ahead with Marklin digital, it may be quite an initial expense, even in a starter set. Please note that you cannot use the wired remote if you use an MS2 (or MS1 for that matter).
4. I would not worry about digital turnouts for now. Unless you have turnouts far from where you are sitting, they are not necessary. I had to buy a separate set of digital turnouts that work very well for this reason, but otherwise, why pay the additional money?
5. Blue transformers are a fire hazard - please do NOT use them. You can read up on point in this forum. Buy a used white analogue transformer and you will be free from these concerns.
5.1 These transformers can blow the decoder in your digital loco.
Bottom line: In your shopping list I would put, in this order:
A. White transformer for analogue locos (you CAN run digital locos in analogue mode with these transformers without fear of putting the house on fire or blowing the decoder), see below;
Transformerb. Wirelesses remote controller set; and
c. One or two extra wireless remote(s).
Happy train running.