So, I have, or rather my character has, unlocked the ability to create constructs with half their normal health. At 10th level the cr goes up to 5. I can have either one cr 5. Or a mix or CRs that add up to CR 5. 

At 14th its CR 9,  then 12, then 16 maxing my cr out. 

What is the best construct for each CR, or best combination of constructs for each cr?

What's the cap before 10? Is it anything below 5 or is it some lower number?

Well, either way, my answer is the Bronze Sable, which you can find in Mythic Odysseys of Theros. It's a CR 1 medium sized bronze statue with decent hit points and, most importantly, multiattack and pack tactics. Once you can conjure 5 of these things that's 10 attacks at advantage...  not for a crazy amount of damage or anything, but with the way the action economy in 5e works the sheer number of attacks will overwhelm most enemies more than a more powerful construct will be able to pull off with fewer, more devastating blows. If you get to CR 16 and can have 16 of these dudes running around you've basically got a small army on your side... although your turn in combat is going to end up taking like, a half hour, so be prepared for that.

Thank you for the advice. I get the ability at 10th and it starts as CR 5. Army of Bronze Sables. Intriguing, Thank you! 

Still looking for more cr and such so anyone else feel free to give a monster example

Can I ask how you are able to summon these constructs? Is it a particular spell, or a unique ability? Mostly I'm curious about the duration... if it only last for a minute, you're mostly limited to combat constructs, but if it has an hour or more duration you could focus more on utility and problem solving. Basically any large construct with decent speed, for example, could be summoned as a mount, which is really only useful if it lasts for a decent amount of time.

As for other creatures... a nice CR 4 construct that I really like is the Helmed Horror. It has advantage on all saving throws against magic, quite a few resistances and even some immunities (including against Force damage, which is almost never resisted) and it has a really unique feature where, upon its creation, the creator can just make it completely immune to 3 spells. The Statblock uses Fireball, Lightning Bolt, and Heat Metal as examples, but you can pick any 3 spells you want.

It is a homebrew ability that lets me make the construct or constructs at the end of a long rest. It lasts till i create new construct(s) that go over the CR.

So think of it as I create 5 cr 1s, at the end of my next long rest i can reset that and create maybe two cr 1s and a cr 3.

You get it for the full day? Dang, that's wild... a CR 5 creature is really powerful to have as a companion all day long. If you don't want to manage a small army of rodent statues, a great CR 5 Construct could be a Gold-Forged Sentinel. It's a large creature with a fly speed of 60, making it a great mount. It also has advantage on spell saves and can even reflect spells back at the caster. It even has a recharging fire breath attack.

Yeah.. Though the other players got powerful abilities as well that make mine pale in comparison. Again it is half health. Gold forged sentinel is a wonderful choice for the cr 5. Any opinions on the cr 9?

I don't know if there's any in any other books, but in the stuff that I have access to I can only find two CR9 Constructs, and it's just the "Clay Golem" and "Reduced Threat Clay Golem", which are terrible choices because they have a feature where, if they're ever below 60 HP they go berserk and blindly attack anything near them, which is especially rough if they're reduced to half their Max HP right off the bat.

CR 8, though, has the Warforged Titan. It's basically a giant robot; it even has built-in platforms for medium-sized creatures to ride it comfortably. Could be a huge pain to bring with you depending on where you're going... really cool if you can ride it into an open field like a Power Ranger and wrestle some other giant creature, but for situations where you don't have enough space to bring along the Iron Giant you could take a Living Blade of Disaster... it's quite literally a 9th level spell as a creature. Granted it's a pretty crappy 9th level spell, but it's still basically a small black hole shaped like a sword that can crit on an 18-20, and on a crit it deals 12d12 Force Damage.

Yeah. Have you seen "Fractine"? It's from one of the monstrous compendiums the first spelljammer one. Pretty good construct. Living blade of disaster is neat.

Oh god. I just realized its a potential 384 dmg average.

4 flying swords count up to a single cr 1. So 64 flying swords equals a cr 16. So average damage of a flying sword is 6. So 6 x 64. If my maths correct its an average of 384.