For about $20000 you can get a used, 2-seat trainer which you can fly for your private pilot certificate, instrument rating
That would also be an airplane totally unsuitable for your Instrument rating.
Borderline for your private if you intend to make it a career. Just to noodle around recreationally sure.
Here’s my recommendation: do your IR in the same make and model you do your Private in.
Make sure you know the power settings and the in and outs of VOR navigation. This will save you a lot of aggrevation during your IR, money too.
Unless you’ve got money to burn owning an airplane is a PITA.
Tie down fees, maintenance funds, insurance and fuel cost.
If you can fly for $100/hr on your own airplane you’re lucky.
So you buy a plane for $30k and fly 250hrs at $80/hr.
You’re now at $50,000.
Now you need to rent a plane for your Commercial add $3,500-$4000 and add a twin for your ME rating at $5000 give or take.
You’re total is $60,000 which is the same you’ve spend if you’d have your own airplane but without the headaches and having another airplane available in case of maintence issues yadayadayada.
Buying an airplane for your training being cheaper is a case of false economics.