There's a few questions to probably ask, some you may not know the answer to but some you will and should.
Do you know what area in graphic design you want to work in? Or the kind of design work you'd like to produce? Do you have any skills in illustration/drawing/art? (you definitely don't need to have those skills but it would probably influence the work you want to create) Have you completed any study? Do you have any skills in any design programs? How old are you? What kind of current experience do you have?
If you apply and get in, TAFE is certainly a viable choice not to mention potential to save yourself extra years of debt. Cost obv. shouldn't be the only factor here but there are simply no guarantees wherever you go.
If you don't get in, you may want to consider taking a year or two to work or travel - if you recently out of school I would suggest that you would get more out of it with a broader perspective/life experience.
I'd suggest creating a shortlist of schools and then go to some open days, graduate exhibitions and talking to students and faculty staff. Talk to other people by all means but just be aware when you talk to course coordinators, sales, marketing - likely to be working for commissions.
Go armed with a bunch of questions ie. links to industry, how many hours face to face per week, access to lecturers, class sizes, how much of the course is done "online", ratio of class to "studio" time etc etc.
One option to consider is doing a Design Fundamentals bridging type course to see if you like it. You'll have a year under your belt and then you might have some more options for going f/t.
Regarding your question about choice of schools for hiring - I think you'll get a different answer depending on who you ask. I haven't in the past and I certainly wouldn't show any bias in the future towards hiring a graduate from place A over B, C or D - I went to private but honestly wouldn't care too much where a student graduated other than it being a point of conversation.
Most of the places are teaching you the fundamentals. The rest comes down to luck/timing, aptitude, attitude and work ethic. If you have some other interests and kinds of experience under your belt, something a lot of employers look to these days, I would suggest that would give you more of an edge over another graduate than say where they come from. Just my two cents.
Best of luck with your studies, let us know how you go.