Howdy and welcome to the shooting forums.
1 - Based on your post I'm presuming deer only, so anything in a deer legal caliber will suit.
Deer legal caliber specs below:

The most common are 243 and 308. I would personally steer clear of 22-250 as only some of the rounds you can get for it are deer legal.

Good starter deer rifle brands would be something like Bergara B14, Remington 700(older ones for preference), Tikka T3(and T3x), Howa 1500, etc. Best bet would be call into a few gun dealers and see what they have in a deer legal caliber and that fits you well, feel good in the hand and in the shoulder, etc.
List of dealers by county here:
https://www.boards.ie/discussion/2057601456/registered-firearms-dealers/p1

If it is your first firearm you will need to prove that you are "competent" to use it as part of the application, which here usually means a competency course(1 day in duration). These are run by Country Sports Ireland, the IFA(who do a discount if you are a member I believe), individual gun dealers and the NARGC. I do not recommend the latter because the course content/quality can vary widely from club to club that runs them.

2 - Nope, you do not need to join a club, especially if it is for shooting on your own land.

You will need to fulfill the criteria as set out here to get a deer hunting licence(in addition to your firearms licence):
https://www.citizensinformation.ie/en/travel-and-recreation/sport-and-leisure/deer-licences/

One note on that, you will need to do the deer stalking course before applying for the deer hunting licence, so you might enquire with a deer course provider(CSI, IFA, etc) whether that proves competency with a firearm for the purposes of firearms licences(I would think it would do so since there is a firearms theory portion and a live shooting portion of the deer course). Then you wouldn't need to pay to do both competency and deer stalker courses.

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Now with all the above in mind if that does sound like a lot(it is, to an extent. Competency/deer stalking course, firearms licence, cost of firearm(and silencer, scope etc if chosen), deer hunting licence) but there is a thread here where you can advertise for deer hunters:
https://www.boards.ie/discussion/2058285623/deer-leases-2024-2025/p1

Mostly it is lads looking for leases but you can post there advertising a lease to shoot on your land, just note the rules for posting in the first post.
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That all said if the above makes sense then awesome, if not then post up some more questions or if you are wondering about any aspect(silencers, scopes, references, calibers, etc) then ask away, the posters here are a wealth of knowledge and very willing to help someone starting off.

So the process buying from a gun shop would be you go and pick the gun, put a deposit down and the dealer will give you a note with a serial number and their dealer number.

You then fill out a firearms certificate application form(FCA1) and hand it in to your local garda station.

Then they will send a crime prevention officer out to check you have a safe, make security recommendations etc.

Then you will get your grant letter in the post, which is essentially a request for payment of €80. Pay that and your licence will arrive by post within a week.

Bring your licence to the dealer and they will hand over your firearm in exchange of the balance of payment.

In short, yes ;)

I have heard that before but never learned whether it was actually law or spurious.
The version I heard was landowners didn't need a deer licence to shoot deer provided it was only on the land they owned.

Sorry I don't want you to be under the wrong impression, that is what I heard but haven't been able to find it in either the wildlife acts or the firearms acts, so I would not be planning on pursuing that path until you have a definite answer, along with a look at the actual law which underpins the answer.

I doubt the NARGC would have an idea, but you might reach out to IFA countryside, since they have a large number of farmers they would likely already have asked the question.
https://ifacountryside.ie/

You could also reach out to the NPWS and see what they say, since there is something called a Section 42 licence which allows deer to be shot out of season if they are doing serious damage:
https://www.npws.ie/licencesandconsents/disturbance/stop-damage-flora-and-fauna-wild-animals

At least one of the two is likely to know, and since the NPWS issue the licence and you have to be the landowner to apply for it you would likely get an answer there.
But again get it in writing, preferably with a link to the appropriate legislation to ensure you are legally covered.
It will also help you justify your reasoning to the Guards when you go for a licence if NPWS have sent you such an email/letter.

There was also this article from 2016 calling for farmers to be allowed to cull deer on their own land:
https://www.agriland.ie/farming-news/should-farmers-be-allowed-to-shoot-deer-without-a-licence/

Which I suspect was a call to do so without using Section 42 licences or similar.