I'm having trouble linking my bthrow's on characters mid-weight and above.
Oh no, I see trouble brewing. Based on the post (and what most people try to do when they pick up ICs), I'm guessing you're doing a P Bthrow > N Regrab.
If I tilt it too much , nana runs.
You'll need to clarify what you mean here. Does nana connect the regrab, but slides after the dash grab away? Does Nana whiff the grab? Either way, both of those typically happen when you grab slightly in the former situation and extremely late in the latter situation. In most cases, unless you're trying to go tripless (see next section), it's easiest to time it so Nana pivot grabs, which the game will automatically do for you if you simply hit grab earlier in your motions.
If I tilt it just a bit, nana turns around twice (original direction).
This is a documented phenomenon of the soft-turn CG. What is happening is that the sync mechanics force Nana to face the direction Popo faces, and Popo flips directions at some point during the Bthrow animation. The game originally reads Nana is walking a certain direction, but then it realizes Popo flips so Nana now faces the opposite direction, only to recognize later that you're holding the opposite direction from which it flipped you. To alleviate this problem, you can input the bthrow for Popo softly enough so that nana does run, and then let go of the analog stick and let it reneutral since the game will turn Nana around for you without any of your inputs! You can test this by holding shield while trying to CG: it's possible to actually input a Bthrow while tilting nana's shield WITHOUT rolling. Nana will actually remain in shield but switch direction allowing you to shield grab, which is one way to address the constant flipping of direction as well. Be warned though that the lighter the character, the more unviable this method becomes. Some characters "flip of nana" occurs within a couple frames of when you should be grabbing, creating a 50/50 scenario if Nana will even grab in the correct direction.
How do I make it more consistent?
I'd suggest learning to CG in a different method. I'd suggest using one of the tripless variants. If you need a turn around, throw do a P F/Dthrow to Nana Regrab and follow that with a N Bthrow > P turn around and grab. I'd then begin practicing paying attention to both timing AND spacing. Most ICs when they pick up the character think it's only timing, when a majority of grabs dropped at a high level occur because of spacing issues.
TLDR: Do the Bthrow with Nana. Turn around grab with Popo
Which character should I be practicing on (so far I'm practicing on Lucario)?
All of them. I'd practice in frequency of the characters you are going to play against. If you don't have any specific matchups you're facing, I'd practice more on higher tiered characters and bad MU characters. Make sure to practice on ZSS because she never shows up on random and a lot of ICs neglect to do so.
