I don't know anyone who has had good luck with RIRs.
		
		
	 
Then you don't know enough people.  No matter the breed, whether RIR, Orpington, Silkies, Barred Rock, Polish, or any other you can find stories on here where they are either sweethearts or devils.  What has been your direct experiences with RIR's or are you just copying something someone else said?
	
		
	
	
		
		
			I'm considering getting pekin bantams but I'm concerned that it may be a bad idea due to their size compared to the size of my current 3 pullets: 1 orpington, 2 sussex.
		
		
	 
To me, there are two parts to this.  Each chicken has its own personality.  Some tolerate other chickens better than others.  Some people have flocks with bantam mixed with full sized fowl and it works great.  Others have flocks of bantams with the same breed of bantam, Orpington with Orpington, RIR with RIR, or any other combo or similarity that are horrible to each other.  Usually that is one or two chickens acting bad or one specific chicken they are picking on but you can see about anything.  Some flocks of any breed can have bad personalities or great personalities but that is more to do with selective breeding for personality or ignoring personalities when selecting the breeders.
The other part is room.  If you have a lot of room you usually have a lot fewer problems integrating.  But you still have to work with your birds.  How old will the new ones be?  How old are your current chickens?  I usually start with newly hatched chicks.  Until the new pullets start laying I generally have two separate flocks.  Actually, since I often have different aged groups I'm integrating I may have 3 or 4 separate flocks.  The more mature birds can peck the less mature so the younger quickly learn to avoid the older.  I have enough room that they can do that during the day.  At night my coop is big enough that they can sleep separately, plus I have a separate coop where some can sleep if I need to use it. 
There is a lot I don't know about your facilities or your birds so I can't get much more specific than this.  But in general I do "see no touch" for a while, have widely separated feeding and watering stations so they can all eat without being bullied, and try to not put them in tight quarters where they cannot get away if they need to.  And I observe.  I watch to see if there are issues and deal with them if I need to.  But I hardly ever have issues.
	
		
	
	
		
		
			Let me know if this is a doable feat or if I need to abandon ship. I don't want them to get picked on
		
		
	 
You are dealing with living animals.  You do not get guarantees with their behavior.  It is possible any of them can be picked on.  It is possible none will be. 
They will determine a pecking order, that is a natural part of a chicken flock.  That might involve bullying, fighting, or intimidation.  I don't see that as being picked on, it is a natural step so they know their place in the flock and they can live peacefully together.  My goal in integration, determining the pecking order, and just in having a flock is that no one gets injured.  I'm OK with them occasionally having a small squabble as long as no one is injured.
	
		
	
	
		
		
			I am also ordering easter eggers and a commercial breed mix of hyline/Rhode Island reds.
		
		
	 
If they are all baby chicks the same age I'd try integrating these with the bantams right from the start.  Do not squeeze them into a teeny tiny brooder, give them room, but I think you have a decent shot at success this way. 
Good luck!