I think any way you do it is going to end up costing quite a bit, it’s Lego 😃
You could do it virtually on CAD (Bricklink Studio probably the best) and then just order the parts you need (brilliantly BL Studio will take your design and automatically work out the cheapest way to get all the bits from all the different online sellers). Especially handy if you’re new to Technic and aren’t really aware of all the different options.
As above just fill up a few virtual shopping carts on Bricklink with a wide range of useful looking stuff.
Otherwise eBay for job lots of Technic or set up an alert on HUKD and buy any discounted sets (not ones with motors in though unless you want those as they add massively to the cost of sets). You can built the sets first which is a) fun but b) lets you see how the professional designers put the bits together which could give you some useful ideas