Hello and Welcome
*oh darn, you must've updated your build just while I was writing this, anyway. I'll keep the following answer here anyway*
You have some nice ideas for a first time builder. Now I am kinda hoping to throw you in the deep end with what I have in mind for you right away.
But first: this RPG is a lot harder than what you are used to, just for the vast amount of different types of encounters and enemy mechanics you will meet when being thorough, and that is why some builds end up stronger against some of them and possibly pathetically weaker against a few. It is really hard for a new player to acknowledge this and it forces restarts, willingly or not. Especially on higher difficulties it is possible to soft lock yourself from advancing in early game because you were caught completely off guard with something and say you already spent all available cash and resources, or even mess up with not having enough back up saves so that would accidentally screw you over.
Now shotguns and psi are both very forgiving in my opinion and there already is a lot to play around with them in early game, combine them with bear traps if needed. It is fun
I recommend this build based on your ideas and observations on any difficulty under dominating. I would still probably encourage playing this on normal. The difficulty spikes combined with more advanced enemies, mechanics and everything in higher numbers might get demoralizing
I have played something similar to this, with a low perception for shotguns start on dominating to try some harder encounters out and it is still viable. Well anyway, the build's strength and base idea is to sit at <30% health for more pellet criticals and more psi criticals to hugely boost your damage output and position yourself for leading shots every time to better hit your marks. The core feats are are picked 1-14, after that the feats are more QOL and you can just pick what you want more, but the idea there is to boost damage and add comfort. There could be some controversy with 8 int start with this and you could go 6 instead, but the idea was to have one more psi slot and that you would meet the requirement for Psycho-neural Flexibility at 16, and generally have higher effective scores in crafting and hacking earlier. Other than that the attributes meet the criteria; Strength enough for a vindicator and riot armor, Dexterity for leading shots (absolutely critical for any shotgun build), Agility for sprint, Constitution for Survival Instincts, Perception stacking for higher Guns skill, and finally Will is tanked to 3 which we make suffice in non-thought control hybrids.
Start out at 5-5-6-9-4-3-8 with more accessible psi and crafting with Psycho-neural Flexibility and one more psi slot, or 5-5-6-9-6-3-6.
I tried not to meet any specific skill caps, but there is the general idea.
Enough Throwing is what you think is enough, there are no throwing specific feats included so take some.
Stealth (even if unwanted for the core build) to lay bear traps before a tough fight or for those special occasions that you really want it to complete a quest for example. You don't need to invest heavily in it, just add some points in and get high effective stealth from balaclava+stealthy leather armor+ninja tabi boots.
I usually like to get rather high hacking skill early, but would not go over 135 effective.
Effective Lockpicking of 45 is enough for omni-tool to open all ventilation shafts, higher than that gives more access and more loot, but I don't find it critical. A flavor choice.
Pickpocketing is for extra pennies, sometimes in form of ammo, but mainly adrenaline shots and oddities. Completely optional.
Traps would be for setting, detecting and disarming them, also totally optional to put points in. You can blast mines with Pyrokinesis if you know they are there, but cannot spot them.
Persuasion is a flavor choice again, but as you had the idea of getting the Shoddy early, my advice is to go with just enough assigned points in it and to have Mercantile synergy boost cover the needed points. More simply, take 18 in persuasion and go 20 mercantile early so you hit (20) in persuasion, that is if you never intend to go higher - you can finish the game with 0 persuasion. For a fast level 2 on classic, you can make your way south from Old Jonas and crush some bugs, and make your way west and bash some hoppers - and then go talk to the quarter master for your shotgun. 20 effective persuasion is required for that. Why I mentioned this is you can also use that 20 Mercantile before you ever go to the Pens level to talk to the Metathermics trainer to get two freebies instead of one.
Higher Mercantile is to open special stocks for some vendors and it is some times used in conversations for discounts and such, never needed to go crazy high, but effective 105 is what I recommend.
Get started with crafting - early game tips for this build:
For your FIRST crafted Tactical Vest, find and buy: Psi beetle carapace, laminated fabric ballistic panel, insulated vest (component) and black cloth - a flavor choice again, but it looks cooler and offsets the stealth penalty by adding some.
For your first Taser: Electroshock generator at lowest quality possible for low energy cost, and Plasma Core at around ~30q.
For your first shotgun: a vindicator shotgun frame, at what quality you can afford to find and have skill for, a forward grip and a short barrel. Prioritize spread and damage, shotguns are lethal even at ~30% to-hit chances if you stack critical chance
Supply of repair kits: 25 or 50 effective in mechanics, electronics and tailoring to craft. Scrap unwanted metal, fabric or electronics for a constant supply.
Stuff is pretty heavy so you can pile them up in any location you prefer. Items won't disappear even if you store them in the middle of a busy street in a city. Bodies however do disappear so if you are undecided if you want to hang on to some stuff, you can loot a body and drop their belongings on them. That way you can preserve them.
Even that it doesn't say it in the build planner, Psycho-temporal Acceleration feat has a prerequisite of knowing either dilation or contraction. It might put you in a tricky situation where your assigned points in temporal manipulation are sub 25 and you are leveling up to 12 and you just reeeally want the feat there and then, but cannot actually learn that.
Anyway there is the feat order I had in mind for you; and this is for the 5-5-6-9-4-3-8 variation. Lower perception early has the disadvantage that you will not immediately spot traps and something hidden, but it does get better as you level up.
https://underrail.info/build/?HgUFBgkKAwjCoDgAAAAAUDweMgBQUA8oUAAAwqBGAABNOWIrwrA9KsKWLsKHS8K9LCYnMcK1wqQo378