The cheapest deals come from using what every other builder uses.

As your partition rises to 3m, I'd suggest using 47x95mm studs - a
typical cost would be £1.20 to £1.50 a metre - obviously cheaper the
more you buy.

Standard spec would be "regularised and treated" - this means its been
"hit and miss" planed so no dimension exceeds the spec, that the
corners are rounded off (makes for nicer handling), and it's been rot
treated.

Get 4.8m lengths delivered, and chop them to whatever you need. You'll
easily use up the offcuts for noggins etc.

Typical low-cost sheet materials are structural ply, or OSB3 - both
around £25/sheet for 18mm thick in smallish quantities.

Again, I'd uses the thicker, heavier stuff right the way through - the
cost is marginal, and you'll get the durability against hard knocks.

The only thing I would check - is whether the timber treatment is any
kind of health hazard to animals.