Congratulations on getting engaged!!
I had a civil ceremony in 2016. Everyone loved it, even my old parents, who are also religious - thankfully they don't put any pressure on us about things!
To answer the questions you asked, yes, you have to ring up your local HSE registrar to arrange an appointment with them to go down and register your intent to marry, which you have to do anyway, regardless of whether you have a civil, humanist or church wedding.
You have to give at least 3 month's notice to the HSE, but if you want one of their registrar's to perform the ceremony, I'd ring them immediately to see what dates they have free around the time you're planning for, as you'll be caught in a cycle now of seeing what venues are available on what dates, and then whether the registrar is also available on the same date.
You will have to pay - I think it's €200 - to the HSE to register your marriage, regardless of what kind of ceremony you have, and if they do the ceremony for you at a venue outside of their HSE building, you have to pay them mileage. I think I paid something like €310 in total to them for my wedding.
The time slots they perform ceremonies are are technically set in stone - 3 o clock in the afternoon is the usual time, but I'm fairly sure you can also have midday. But they are the only times they do (unless your registrar is just really sound and unofficially agrees a different time) and they have to be done on a weekday (basically they do them during office hours because they are HSE employees)
The venue also has to be on their approved list, so most hotels are ok, they've already gotten approval, but if you are thinking of having the ceremony somewhere more imaginative than a hotel, then the venue has to go about getting approved by the HSE first, so again, you need to get cracking on things like that asap, just in case there's any snags.
Readings, songs etc absolutely cannot have any religious content, but they can be anything at all other than that, which is nice for people like me who can't stand religious readings. I had great fun Googling my readings and had a list as long as my arm to choose from.
You are pretty much limited to 2 readings and maybe 3 musical pieces, but again, in my experience, the registrars are lovely, they want you to have a nice wedding day, they're not going to be too strict, as long as you don't take the pee and make the ceremony an hour long!