I'm going to provide two options here--one that is a strict answer to your question (highest damage that meets your criteria) as well as an alternative that provides more reliable damage, along with a special feature that can aid your allies.
Brown Bear AC 11 and HP 34, and packing a Multiattack that, if you hit with everything, hits for d8+4 and ...
Pure monk has more attacks with similar mobility
Rogue and monk don't multiclass very well
Rogues want a single, accurate attack. Monks want many attacks. Rogues gain a Sneak Attack die every other level. Monks gain a ki point (and thus a use of Flurry of Blows) every level. Rogues can Disengage as a bonus action for free. Monks can Disengage as a bonus ...
The obvious candidate: Evasive Footwork
When you move, you can expend one superiority die, rolling the die and adding the number rolled to your AC until you stop moving.
This is probably the best one on the list. A good roll on the superiority die can mean you are nearly untouchable for the duration of your move.
Honorable mention: Parry
When another ...
Although we of rpg.stackexchange are happy to answer your questions, I want to note that there are some really good player-created guides that answer this specific question. For example this Practical Guide to Wild Shape seems pretty good.
At CR1, it recommends the Dire Wolf for the reliable advantage and trip. It also offers reasonable suggestions for ...
You've got options!
Before I begin, I do want to note that the Martial Adept Feat only gives you one superiority die/short rest. This isn't going to be used all the time, so it's about when it can do the most for you because it's not happening all that often.
What you're describing is a character that is very good about moving around from creature to ...
Another option to consider at CR1 is the Giant Spider.
Deals 3d8+3 damage
Has a web attack that can restrain enemies. Your allies attack a restrained enemy with advantage on the attack.
Can climb around on walls and ceilings, which is fun and gives a lot of options and helps make up for the lower HP (only 26).
This is my personal favorite ...
Focusing specifically on your use case, where you have 2 full hands, and want to cast a spell with a material component requirement.
I don't think that your DM's ruling is supported by the rules in 2 ways. The first is that dropping an object does not appear to use up your free object interaction. Jeremy Crawford has tweeted
The intent is that letting go ...
A likely contender is sofawall’s “The Cube” build—except it was never posted fully in public, and at least some of its secrets have been lost. This post details some of it, saying
The Cube? That was me.
Wall of Force
Magically Hardened Obdurium
It can move. As it still a build in progress, I will say little, other than the bare-...
You can create an unlimited number of permanently controlled skeletons, but at a slow rate.
First, create zombies using Finger of Death. These zombies are permanently under your control. As a level 20 wizard, you can cast this spell 5 times per day, leaving you with your level 9 spell slot.
True Polymorph the Zombie into a Skeleton and concentrate for 1 hour....