When I asked for the relevant rules we have to follow, I didn't mean all the Sasori rules. It's just that a few of the rules we have to follow are in that list for some reason. As standard puppeteers, we can't create Human Puppets and we're not Sasori so a lot of those rules don't apply to us. But anyway, I'll go over the ones which do apply to us.
You can't have a KG/HA or SM/8IG in the same bio. You can however mix puppetry with sensory or smoke.
Pretty simplistic, you can't put in the same biography anything other ability which constitutes as a Kekkei Genkai like Ice or Storm, a Hiden Ability like Nara or Inuzuka, or Sage Mode/Eight Inner Gates. I know you're newer so this doesn't really apply to you, but it's just something to keep in mind for the future if you ever wanted something with Puppetry.
Puppet users may not have shadow clone (other kinds of clone can't control puppets.)
To be quite honest, I'm not entirely sure why this rule is in place. I have a couple theories about it though, discussing it with others. Firstly, Shadow Clones can use any jutsu the user knows, including the Puppetry technique which would be like having more puppeteers for someone to fight against. Secondly, this technique could be considered overwhelming for the other person, having to fight five of one person, with puppets on top of that which would give you a great advantage. The third reason I can think of is that the original puppeteers were never shown with such an ability, so it might stem from that. Regardless, you're not allowed to use standard Shadow Clones. However, since there's a plethora of other clones out there for you to use, you're allowed to use them instead for your techniques.
Only 3 puppet summons may be active at any time. (for example you can have the 100 puppets that sasori summoned [as this classes as one summon] and 2 more puppet summons.)
This is more of a control-based issue rather than anything else which might spring to mind. You've only got ten fingers, so you can only theoretically use ten puppets, but only Chiyo was shown with enough skill to do that. Three puppets is the maximum we can use and kee control over. Though this only applies to three different "summons" per se, Sasori's Parents although they can be summoned seperately only count as a single puppet summon. This rule is always followed unless specified otherwise in the technique, such as Chiyo's Ten Puppet Army of Chikamatsu which is the only puppet which can be out when used.
Only a maximum of 2 puppets summons may be performed per turn.
This is because you have to perform the puppetry technique where you create chakra threads as well, or you'd just have lifeless dolls sitting there for a turn. Consider this more of a guideline than a rule you have to follow, or you'll have a whole turn where nothing happens apart from lifeless puppets sitting there. Though don't count on me for this, but I've asked around and if you're physically carrying the puppet like Kankuro used to in Part I, they can be brought out passively and it not counting towards the limit of techniques per turn.
Any question regarding this so far? If not we'll continue.
Also I recommend you reach Chuunin level (200 posts) before we continue, otherwise I can't teach you about the puppets you can use, and by extension their techniques.
