Forget the canter for now... what you need to focus on is the walking and trotting like everyone else is saying. I've just recently backed and started my first horse by myself (ie, I'm the one doing everything, my gelding was my first horse I backed, but had a friend start)... so I know what you're dealing with.
Honey would just randomly put on the anchors and refuse to go forward. The first thing to say is : don't get off. Simply turn your horse and push forward. If the horse still wont move (I know, its frustrating!!), keep turning... if you still dont get result and you're firmly asking forward, gently slap the end of your excess rein just in front of your saddle on her shoulder... it's to make a noise, not to hurt. I've only had to do that twice, and only resorted to it after like twenty minutes of no movement... Honey soon learnt that forward was what she needed to do (she's the typical "yay look at me go" kind of horse, who enjoys her rides and thinks she's super cool cos she can do it haha)... she tried it once in the trot, out of no where she slammed on the brakes and just stood there... its just a baby "but i dont wanna" and you have to be the one to encourage forwardness.
Straightness is a time thing, it also depends on how much this horse is accepting legs on its side. I kept it simple in the beginning with Honey's training, and introduced the leg aids in once we had been walking for ages and just started thinking trot. I used my legs to ask forward and to balance the halting, but to promote straightness I wasn't too concerned in the first few weeks. Once she was okay with the idea of me being there and doing what I was doing, the leg became more important. Make sure your horse is good with the leg, ie, can bend around a corner correctly with leg support and not so much aiding with the hand... again this is a gradual thing, some horses take longer to pick it up.
You sound like you really need to get a bit firmer with your leg aids... I was taught that if a horse is kept forward enough the horse doesn't have the chance to be too distracted... keep it interesting, change it up, make sure to be forward all the time, with lots of praise... sounds like you're doing a great job with your mare, it will all come together with time!!!
Good luck, looking forward to hearing how things go! Oh and don't forget to use voice commands that you do when lunging!!!
♥ Seoul Searchin' for the Lovebug ♥