You definitely need a bodkin or two, it's really just a stiff needle that helps with many things. You can make your own, but a dubbing brush or two is a pretty essential tool.
Take a look at the JS Tools at Stockard, they are cheap but a hair stacker doesn't really do anything except hold hair when you bang it on your table. Spend your money on good scissors; tools that do not have working parts and thus the cheap ones are just fine are: bodkins, bobbin threader, hair stackers...even the dubbing twisters and hackle plier don't have to expensive. I am actually going to buy some of these as back-ups... JS Fly Fishing: Rod Building, Fly Tying: Just Simply Tools Economy Hair Stacker
I have a couple different scissors that I use but I have been doing this for 12 plus years now, so you can build up to this. An old pair to cut wire, one I'll use for snythetic materials, and one for natural materials. The pair for natural materials is my best pair, I like the Anvil Ice. You could get a cheaper pair for synthetic materials from a craft store.
Whip finisher, a Martarelli style is easier for me, and possibly in a couple of sizes. Truth be told, you can throw a couple of half hitches in and add some head cement. Or you can look at some of the videos and learn to whip finish by hand.
Ceramic bobbins are recommended.
Learn to wrap hackle by hand at first, add hackle pliers if you need them. Here's a good read on hackle pliers.
Aside from the tools already mentioned, I find a good light and magnifying lens to be essential for tying. It needn't be an expensive light. Mine is a halogen desk lamp from Ikea, and I bought it for around $10 several years ago. My magnifying lens is made by the people that make Peak vises, and was about $35. It can clamp to the vise stem, or to the vise's pedestal.
Another nice tool to have is a little squeeze bottle for head cement. I started out the "traditional" way: open bottle of head cement, dip in bodkin, dab on head of fly, and repeat as needed. That takes forever, and can be a smelly mess.
One other tip... People tend to wrap way too much thread on a fly when they're beginning. WAY TOO MUCH. If one wrap will hold material to a hook, then so be it. I was just as guilty as anyone else, and went through miles of thread before realizing that enough is enough. Since you're looking at YouTube, take a look at Davie McPhail's tying. He is very careful not to use one wrap of thread more than necessary, and that can make the difference between tying something that looks like a ball of yarn, and something that you will be proud to have tied.
Here's one of Davie's videos. Pay attention to the way he wraps thread, and attaches materials to the hook.
The Guys have covered what you will need quite well,also you don't have to buy all Top Shelf Gear,unfortunately that's all you could buy many,many years back,I've found over The years most of The Cheaper Copies do The Job.
Even though I have 4 or 5 size Hackle Pliers I find I mostly use The smaller ones.
Also you can't have enough Bobbin Holders,I've about 20-25,mostly cheapies as I find it a Pain looking for one to hold Cottons etc,then I haven't enough..
Another Thing you will definately need is Dubbing Wax.
If you're going to spend all that time tying you'll want your flies to last. While not tools, these two tips I got from the local fly shop have made my flies last longer:
A bottle of loctite (in the grey bottle). Put a bit on the thread every once and a while. It's like superglue but thicker consistency.
On flies that use a palmered hackle, one of the last stages take some very light mono (even sold on spools) and wrap counter direction of the feather so it crosses over it. Keeps the hackle in place and if a toothy fish nicks that feather it won't all come undone. If you take a close look at a $3.00 woolly bugger you almost certain to see what I'm talking about.
Since I use Sally Hansen's hard as nails I don't use my bodkin that much. But when I did I made sure to stick it in a medicine bottle full of steel wool with a whole punched in the lid....helps keep the dried head cement from building up.