How long is a piece of string?

I am sure that if you are lucky you will get many points of view ,well  you would if the forum was more active, and players wanted to divulge their expertise.

Most of the basic information can be found within the game,and if you search the forum for old posts, you might gather some more insight.

The basic function of the Manor is to produce silver, but it also functions to speed up training troops, and there are other things that will do this too.

The Infirmary is to heal and/or resurrect  your troops.

To resurrect  troops you will have to spend gold,a whole topic on its own, healing is cheaper, but if you do neither of these things you can get away with no infiirmaries, except  the game forces you to upgrade one building in order to upgrade something else,.and once you have built an infirmary you have to have a minimum of one.

Remember troop casualties in town, go to healing, those outside  mostly go to resurrection, dependant on any bonuses running .

If your shield fails, or you are using the town as a trap, you need beds to cover this event, unless as stated before, you are prepared to just train replacements.

Be prepared to change the set up of your town as you progress in the game, or switch strategies ,eventually you might decide  on one infirmary, and the rest manors, you never know what and when they will add something new to the game, or more levels.

You might not even have to worry about any of this if you quit the game sooner than later.

Short answer - War Bloc, 1 Barracks, 1 Infirmary, 13 manors

Long answer

All that barracks does is train troops. So  let's say 1 barracks trains 5000 warriors, 2 10,000 but twice the time, etc.

What manor does is reduce that time. This adds up so let's say 1 manor gives 30% speed up, 13 manors gives 390% speed up.

Usually you want to train a lot of troops quickly so you are going to use boosts. Having more manors means using less boosts but you will have to click a few more times.

If you look at stats for big players / clans you will see that they don't do a lot of healing or resurrecting.  Healing only gives around 35% of the points compared to training and I don't think there's any hero gear or special boosts to save time. The Infirmary Capacity is the number of troops you can heal, the number of troops you can resurrect is much greater but I don't know the limits. Resurrection costs gold. I would only do it if absolutely necessary.

Compared to Knowledge, buildings are cheap and quick. If you build more than 1 manor (or barracks or infirmary) and you find that it's not working for you, you can demolish the extra and build either of the other two.