That would cost less. A new hard drive would be as little as $50 and a newer version of Windows will be another $100 or so. You're probably better off going with Windows 7 rather than 8 because your computer will almost certainly run 7 but is much less likely to run 8.1. Windows 8.1 has a couple of hardware requirements that cut out a lot of older computers from being able to run it, and if yours runs XP, it's likely it won't work. I just looked at Newegg's email they sent out a couple of days ago, and if you're really on a budget you could do it all for a little over $100. They have a refurbished 160 GB hard drive for only $20 and Windows 7 for $85. I probably wouldn't go with a refurbished hard drive myself, but it would probably be okay. Just go to Newegg and click on "latest email deals" at the top. At the very least you can save a bit on Windows.
As for your other question, a wireless keyboard and mouse should plug right into a USB port. So they should be fine with the laptop. If the laptop has a VGA/SVGA port, you should be fine also. I'm using the wireless mouse/keyboard (bought 2004) and monitor (2011) that I bought for my XP desktop computer to write this on my Windows 7 laptop right now.
The machine with the bad hard drive was running Windows 7, though it only has 4 gig ram. The machine I'm on right now is only 2 gig, so I know it won't make it. And the laptop I saw was 6 gig with Windows 8.
Ram is simple enough to change. Do you know if the old machine was maxed out on RAM or could it handle an upgrade to a 4 Gig chip in one of it's slots?
I've not taken a look inside it in 4 years, so I don't know. My vision is so bad I have to be right on top of what I'm trying to see/read unless it's really large. I think I can handle swapping a drive if I pay careful attention to all the cabling and mounting brackets. Installing Windows shouldn't be a problem, though I know it can take a few hours. The cd/dvd drive was still good and was what I using to watch videos until the machine died. The dvd drive on this machine is too slow for videos. I may have to wait until my money arrives later this week, pay the rent, phone, some other bills, then see how much I have left to spend without starving before May. Fortunately, a local mom & pop convenience store lets me run a monthly tab because I've patronized them for 15 years. ETA: And just spoke with a friend who knows a guy who works on machines, so he'll see if that guy has anything available.