Oh ouch. This one is a tough project, the joining the border to the body. There is no 'best stitch' IMO. Maybe very very careful weaving back and forth from one edge to the other would work, taking great pains to take teensy stitches.
Many knitters over at Ravelry are complaining that it's very difficult to join this garter stitch band to the body. So it's not just you!
You're sure right....the border just won't lie flat. It's tricky.
Click this link below and see what another knitter did as a PLAN B:
I really like what she did! It looks good from the Outside and the Inside! And personally, if I was going to knit this adorable baby bolero, I'd do what she did! I'd skip that separately knit garter stitch border that needs to be seamed onto the edges all around!
A lot of those that tried doing it the way the pattern indicates....well, few of them lie flat, and most of them are a hot mess on the inside view. Ugh. And the knitters themselves don't mind saying so.
BTW...185 knitters over at Ravelry have made, or are in the process of knitting this baby bolero. I haven't read through all 7 pages of notes each knitter might have shared....but I suggest that we should! We might find more tips for that border! Plan C, Plan D, etc.
I do this on a regular basis....read thru all the project notes that other knitters have taken the time to share. It's saved my 'bacon' many a time! I've avoided problems, and/or I've found remedies for problems!
I'm back! I've seen another great Plan B! Click link below!