My family will likely be moving to Basel over the summer. At the time our children will be 7.5yo (entering 2nd grade) and 2. Even though private school would be in large part be paid for, we are leaning towards the public school option for a variety of reasons, primarily due to the opportunity for our children to have a truly bilingual foundation if we stay for any extended time (which we aren't necessarily planning for but are open to). I'm not worried at all about our younger child, and not really worried about our older one either . . . over the long term. Though, he loves school and is very social, and I worry that those first few months would be a bit of a shock, especially with trouble making friends, during what was going to be a stressful time regardless. Any recommendations from folks who have put their children in public school starting around that time? I know the public schools seem to have a reasonably strong program to accelerate one's German, we'd just love to get ahead of whatever we can so that he continues to enjoy school and has as smooth a transition as possible. In the meantime, he's joined us on starting DuoLingo . . .
I don't know how they do things in Basel, but if you do go down the public school route, I would ask already now which year he will go into and what the integration program will be. Eg in Zug if you start in year 1 (at 7) they just put you in with normal classes, whereas if you start in year 2 (at 8) or later, you do a year of separate classes to learn German.
Again, i can't comment on schools in Basel, but generally public is better than private for integration. The downside many people see in Swiss public schooling is that it's much slower academically in the early years (but picks up later on, particularly if going to gymnasium).
But then your son will need time to catch up with the language, so this isn't necessarily a bad thing. Bear in mind that he will essentially be learning two languages: Swiss German dialect spoken on the playground and High German spoken and written in class. It will take some years before he is fluent in both!
In Basel (Stadt), the kids are not put into a separate integration program at the primary level like some Cantons. Instead they are pulled out of their class (sometimes solo, sometimes with other kids) into a special German session multiple times per week. Our older child had one year of this and since hasn't needed it. Our younger kid (now in 2nd grade) is still attending one pull out class per week.
Depending on the neighborhood, you'll find plenty of English speaking kids around. Ours switch back and forth depending on who is outside playing -- if a non-English speaking child joins the group, they all switch to German. It's pretty cool.
Kudos to exploring the public school option -- highly recommend it!
Edit to actually answer your question: I think at that age the easiest thing to start with is some vocabulary. Don't stress about it too much as you want moving to be an exciting experience for your kid. Also, very important is that YOU as the parents learn German, and show your children that you're making an effort. The kids we see with the most trouble integrating (language, friends...) have parents who haven't learned any German. The kids quickly figure out their parents aren't planning to stay long term and if the parents don't integrate, why should the kids?
Some kids pick up a new language easily, the majority of them struggle to learn it to a level required for higher education.
Also, if the parents don't know any German, it's going to be even harder for the child, as well as the family because all correspondence from the school will be in German.
I know many families who had children starting public school at age 7 (which is roughly Grade 1), thinking the kids would be fine after a short adjustment period. Generally, they are fine. But as the kids get older and they need a higher level of proficiency to do the gymnasium test, that's when you start to see the large gaps in their knowledge.
Don't want to sound pessimistic, just realistic.
We don't speak German at home at all and there were no problems in Basel. @ThisIsFine gave you great info: the foreign kids are taken out of regular lessons to learn German several times per week. Mine (we came here when she was almost 2) did not need it, but many, many of her friends did, and it is a completely normal thing among kids.
Also in Basel, you will be provided a translator for official discussions with school (once a year). I had one until my German was good enough. When you get letters from school, you can use an online translator, the message will be simple enough, and the same for messages you send the teachers. Many teachers' English will also be good enough to understand what you say.
I have not encountered cases that @cremebrulee mentioned; not to say they don't happen. Now at 13, my kid might or might not get into gymnasium, but it doesn't have anything to do with her German, which is definitely good enough, as her grade in that subject attests to.
Welcome to Basel!