Hi Romantic123
As you will see from my posts, I've been through something similar myself, so I'll give you my experiences and hopefully this will help you.
Have a read of this website on the different types of visas too.
http://www.inis.gov.ie/en/INIS/Pages/Visa%20Types
1) Student visa option.
This is what I tried initially with my then girlfriend (now my wife). However her finances did not meet the required level and because I acted as her sponsor, INIS questioned the real reason for the student visa. Basically they could see that she was using the guise of applying for a student visa to come to Ireland to be in a relationship with me - and to be honest they were right. It was refused mainly because of these two reasons.
Any support of money from you won't be accepted as you are not family or not married. I encountered the same issue. I thought my finances could be used but INIS said a relationship could break up when the two parties are in Ireland and she (my now wife) could be left without an income and require State support.
If she does apply for student visa - my advice and it's only my advice - would be for her have the sufficient finances - either from her savings or a family member. I would encourage you not have her make any mention of you on the visa as in my belief and experience this could go against her. Also make sure she picks a school that is from a pre-approved list of English schools. You can find these on the INIS website.
2) Tourist visa option.
The most important thing with a tourist visa or any short term visa, is to show obligation to return to her home country. This can be shown be a job, study or family (if she has children) and return flights tickets. The visa itself isn't too expensive, its the translation costs - naturally the flights too. In this option you could act as a sponsor, and offer your residence as a place for her to stay. Important things like an itinerary showing places she will visit as well. It is worth pointing out that a visa is only a pre-clearence into Ireland and the GNIB official at the airport can refuse her if they feel they have grounds to. Furthermore the maximum time she can get for a tourist visa stay is 90 days. Again the GNIB official may (and probably won't) give her the full 90 days - it depends on the person and what the assess in their mind about her.
So your option to marry her here during a tourist visa may not work - as I believe you need to give 3 months notice to the register in Ireland - it may be possible to get around this but I am not sure of this.
3) Get married in Philippines
Its what I did (well in Peru).
To be honest and only speaking from my own experience it could save you time and money going this route.
If you do plan to get married in her home country, make sure you follow all local laws accordingly and that the marriage is legal.
Note you'll probably have to go through a similar process of waiting there too before you can marry. This will probably involve more than one trip over there.
Once married, apply for a Join Spouse visa. Processing time could take up to two months - maybe longer I've read closer to a year in some cases. Mine took two months (felt much longer).
In this time I would advise you to find work as you having employment will work in your favour.
There is a lot of information here to take in. I certainly didn't learn it over night but it was from helpful people on this site and others plus my own reading from the INIS web site.
One thing I will say finally is that the fact you haven't met before and your relationship exists via Facebook would be an issue for INIS. They specifically state that there should be several face-to-face meetings and skype, facebook, etc are not counted.
So try to visit her and if possible look at the tourist visa option.
4) Why not move there?
Probably easier for you to go there than her to come here.... just a thought.....
On a personal note - and you can ignore this if you wish - if you get past that entire nightmare of paperwork and she gets her visa into Ireland, one thing to be aware is culture shock. She is leaving her country - a place where she knows how things work, the cultural jokes and faux pas. Do bear in mind that a transition to Ireland where the weather, food and customs are very different could be difficult for her. This was something I overlooked and am now much more appreciative of my wife's difficult move. She'll have to re-learn a lot of things again and you must support her - especially if you get married.
Best of luck and let us know how you get on.