Boy these "inheriting" deals where the poor person is the inheritor can turn out to be a lot of work. Thank you for taking him in
If the vet says the horse is 100 - 150 lbs overweight, I would order a grazing muzzle and get it on the horse five minutes ago. The last thing you need is to have to deal with a horse with founder.
He could wear the grazing muzzle during the day when the sugars are highest in the grass and will spike his insulin levels. These obese horses are Type II Diabetes waiting to happen - it's called insulin resistance in horses.
I use this grazing muzzle on my two metabolic horses and I love it because the nostril holes are so big and my horses don't feel like they are suffocating. Saddles Tack Horse Supplies - ChickSaddlery.com Tough-1 Easy Breathe Grazing Muzzle
As far as a definition for founder - think MAJOR MAJOR gout that can kill a horse or require many many hours of human intervention at the very least.
Don't feed the horse any grain - zero. He could have a ration balancer if you are able to get him in the barn at night.
As far as hay, these types of horses need to eat grass hay NOT legumes like alfalfa or even Trefoil. It depends what area of the country you are in as to what a good, low-starch grass hay would be.
The spookiness is another thing -- it could be he is afraid to be in the barn alone because he's never stayed in a barn; or it could be that coupled with the fact he is in a new place and is afraid; or, if his insulin is spiking on him, that alone can cause anxiety in some horses.
If he can't have a barn companion, I also vote for leaving him out and giving him the option to run in/out of the barn if that is possible.
But he needs to wear a grazing muzzle during the day and they should not be left on 24/7, even though some people do that; his face needs a break
Big high five to you for taking him in and not having any horse knowledge .
Here are a couple links that speak to feeding obese horses, which this horse is if the vet says it could lose 150 lbs Reducing weight in obese horses - Horsetalk - Horse nutrition and feeding articles and information Easy Keepers: Managing Horses Prone to Obesity - Home - Virginia Cooperative Extension
You can Google "feeding obese horses" and get a ton of credible hits. www.thehorse.com
is a health magazine with a lot of on-line information. It is free to join.
Finally, you don't need to keep shoes on the horse, but it does need a steady trimming schedule as keeping the toes short and the heels low helps keep the hooves sound and from possibly foundering. The schedule can vary throughout the year as hooves grow faster during certain times of the year than others.
You might ask the vet for a trimmer recommendation or ask at a boarding barn or training barn. You can always find business cards thumbtacked at the feed store or Tractor Supply but it's best to get a recommendation or two first
Hope this helps and good luck to you with your new Charge