Need advice on what to buy first
I have a 5 year old dekstop with 200GB HDD and 300W PSU. They both really need to be replaced, because the HDD is noisy and PSU can fail at any time. Would a failed PSU damage the new HDD? Need some advice on that. I will be upgrading the whole system, but right now I'm short on money. I can buy a $70 PSU Antec Earthwatts 380W or a $65 1TB Samsung Spinpoint F3 HDD. I'm not short on space, but it would be great to have more. Besides, my hdd is relatively slow.
Well make sure you have your important data backed up, that should always be first priority.
When a cheap PSU dies, it can take nearly anything or everything with it so I usually start with a good PSU. Cheap PSUs often don't have good protections in place and can send a nasty jolt through the system taking out motherboards, cpus, ram... everything basically whereas a HDD, as long as you have it all backed up just takes some time/money to replace and get it back up running.
That aside, 70 for the antec earthwatts 380? It is usually 40 on newegg so you might want to check for another source, I don't know what country you are in but 70 definitely seems high. It is however 1 of my first choices for PSUs on typical business productivity type systems that aren't using high end gaming type components. I do like the 1TB Samsung Spinpoint F3s they seem to run 50-60 here so your price isn't far outside that range for that item.
1) You really NEED neither.
Your psu is working, and you have enough space on your hard drive.
2) If I had to pick one, I would replace the hard drive, on the basis that a modern 1tb drive will be faster.
3) Thinking about it, though, if you have sufficient hard drive space, see if you can't save up enough to get a small SSD for the os and an app or two.
As little as 40gb will do it. Prices are about $2 per gb, and will go lower in time. A SSD will absolutely transform your PC.