Is it cheaper to upgrade my PC or just buy a new one?

It depends on what you need. Advantage of upgradrating your system by yourself is that you can handpick which componets you want to add.
Generally, its more cheaper, but depending on what the user need

What parts of my PC should i upgrade First?

If your computer is old, the following Upgrade is recommend
1. Adding more RAM
2. Install a lager hard disk(In terms of Capacity)
3. upgrade your Video Card.
4 Upgrade your modem and network interface card (NIC)
5 Adding a removable storage devices