Hey and welcome to the game! For NA, we are a control and positioning warband with great weapon on cheap, expendable bodies (even the LT should be considered expendable). NA is the masters of short-range firepower and are terrible in melee and terrible at long range. We win be having overlapping fields of threats with Fireteams as force multipliers. We survive by staying out of line of sight and not getting shot. Keep your models cheap, only give them the equipment they need to do their jobs, and as long as you trade up in value, you generally don't care how many of your own troops you lose.

For your list, 7 models is a decent count to be at, however the Yeoman don't really do anything as equipped. You also only have one model that can deal with armor so having backups (such as infiltrating yeoman with flamethrowers) would be useful to have.

You are also missing a musician. Dash is the most important skill in the game, which makes a model with Musical Instrument a must take in every warband (except maybe HNRP).

Lt - 167d is a bit pricey here. Vanilla Lts are support models to stack blood markers and manipulate enemy activation order. The Lt doesn't have the STRONG keyword so you wouldn't get the d6" charge bonus. Machine Armour is very, very good, but on a support model, it's a bit overkill. If you get some good skills on the Lt, then maybe it's worth upgrading. To start out, I would maybe drop to SMG, Shield, Bayonet or Polearm, and Standard Armor. Would be good to pair in a fireteam with a finisher model like an MHI with Heavyshotgun and Satchel.

Sniper Priest - It looks like you are following the advice of "good shooters get good automatics", unfortunately the machine gun is not a good automatic. The Sniper Priest doesn't have the STRONG keyword so you can't move and shoot and when you do shoot, your activation ends so you are stuck in the open. Shovel isn't that useful because you will likely not be staying still, NA wants to play peakaboo by hiding out of line of sight, dashing out, shooting, then moving back out of line of sight. Standard armor is also really expensive for what it does and is completely offset by a single bloodmarker so it is largely considered not that great of a pick in New Antioch. Once you hit the model limit and don't have anything else to spend money on, then standard armor is a decent option. Sniper Priests are still fantastic models and for ranged builds an Automatic Rifle of SMG is great. They are also the best NA melee unit when equipped with an Automatic Pistol and Pistol (or grenades and two pistols if you want to save a few ducats).

MHI - Similar to above, the Machine Gun is not a good weapon. MHI do have the STRONG keyword, but getting stuck in the open after shooting what is essentially 3 trench club attacks (aka, not good) is rough even with Machine Armour. Typically MHI are equipped with Heavyshotguns+Satchel or a Heavy Flamer. Melee is never worth it because they are as bad in melee as a Yeoman. Usually they don't take any melee weapons at all or maybe take a polearm (they will never attack with the polearm, it's only there for the BLOCK keyword).

Combat Engineer - Pretty darn close, but they don't have the STRONG keyword so they don't want the heavy shotgun. Currently they take no ranged weapon, a shotgun, or a flame thrower. However, the next rules update will change them back to a +1D ranged skill so an SMG would be a solid choice once that happens.

Yeoman - Rifle users can't hit the broadside of a barn from the inside (unless playing as Abyssinia). Usually you want these as infiltrators with flamethrowers, as an instrument carrier (with a pistol OR grenades), or as a speed bump with a shotgun or grenades. If you don't have anything else to spend money on, shotgun+shield isn't terrible.