Please Read, advice wanted.

Okay so for the past three months I have been loaning a 16.1hh appolousa gelding from my riding instructor. He is school master and is truely an amazing horse. But my riding instructor has been nagging me to buy him but I can't afford the price he is wanting, so I am ending the loan and looking for a new 'project horse'.
I have been looking at a 3year old welsh section D mare as I am looking for something smaller than 16.1hh, I was just wondering where I would start with her if I do buy her, she has been backed. But what do I need to teach her, should I do pole work? And with a section d what age should I start jumping her?
Thanks!

Welcome to the forum :)

Here's my opinion and what I'd do if I acquired this same horse. Seeing as she's 3, she's probably just been backed with the basics.
I'm assuming you want the horse to eventually be an eventer - guessing by your user name. I'd start with reinforcing all the horse's skill, moving off leg pressure and giving to the bridle. I would avoid excessive collection for a while more, not all her joints are fully closed yet so you don't want to stress them until she's full grown (around 5-6 years). I would also NOT jump any horse for at least 2 more years. Jumping is very stressful on the joints and a lot for a young horse to learn.
I'd focus on lightness in cues, getting her to give to respond to the quietest and gentlest cues consistently. I would work on things like side passing and bending around turns, responding strongly from seat/leg cues and relying less on the bridle. I'd work on This takes a good deal of time and work for a horse to become solid in. Work on smoothing transitions and keeping her calm and balanced at all times. Horses newly backed take some time to learn how to balance with a rider.
Maybe in many months I'd start with ground poles and basic learning to balance herself. I'd then practice extending and collecting gaits.
I'd hold off on jumping until she's 5-6 years and solid in all these skills.

Judging by the questions in your second paragraph, my advice would be to buy or lease a horse that is already at least partially trained - budget or no budget. At your level of training expertise it is better to buy or lease a trained horse than to buy a greenie that will frustrate you and you will be unhappy with. Too many horses are bought that don't fit their owners, and just end up changing hands...

If she has just been backed, be prepared to spend 6 mos to a year working closely with a trainer on flatwork only.
If this is your first "youngster" then you really need someone knowledgeable on the ground ideally twice a week, helping you bring her along, and who will be able to hop on if anything goes wrong.

Once you have done a few young ones, it gets simpler and easier. I took one from backed to being able to be ridden by his Ammy owner in about 3-4 mos very recently. I'm still working with him 3-4 days a week and she does 2-3 days. That imo is ideal because I can keep him going, but she is still riding enough to get experience.

Good luck and make sure you are hooked up with a good trainer!

Eta about the jumping, I've introduced poles and a small fence, but would not have his owner on at this time (7 mos from breaking) because he is difficult to ride to the fences and unpredictable over them. He will never be a jumper, but for confidence and just incase there is something on a trail, it will be a good skill for him but I think if I worked at it once a week, it would still take a few mos before I was confident to put the owner on. It is really easy to wreck a horses confidence when teaching them to jump and imo should be done by an experienced ride only.

I also agree with Face that if you aren't willing to work very closely with a trainer, a horse who is further along might suit you better.
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I have worked with youngsters before, I was just curious about what other people think, although it did come across as like I haven't done this before. Thank you for all the advice, very sad to loose my loan horse but looking forward to a bright future.

He won't work with you on the price or payments?
Sounds like you already found a good match in him.