First you MUST know where the main shutoff valve is and that it works proper. Try it, shut off the main valve, drain some water from a sink and ensure the main valve does not leak. Got to be able to work on stuff, secure in the knowledge you can totally shut off the water supply.
Number two you must know what you are working on. That does not look like a soldered in valve to me from your pixs. Hard to tell with the quality of the pix and all that corrosion. I looked for evidence of solder but see none. Should see some on the copper tubing. I think it is a compression fitting type valve.
Something like this with the flex supply tube built in; is probably what you have installed there. Only your has that stupid domed handle and maybe is of cheaper quality than these. They do make a solder in female type connection valve, don't think yours is one of them. We should know for sure.
This is the type of valve you want new to replace it. Get something all metal of good quality. Use good braided new flex supply tubes. This shows your typical compression type valve apart in pieces. You will probably have to use the old compression nut / ferrule, not a biggy.
My toilet shutoff valve installed. You want good quality all metal valves, the cheap plastic ones are total junk, more trouble than they are worth. Use the braided flex supply tubes. Well worth the money.
This is what I like and trust for under the sink shutoff valves. Old timers that are all metal and can be rebuilt over and over again if parts age / wear out. IF you are DIY handy, you get to choose your own hardware. These puppies are worth a fortune today.
Yeah, you can hire a plumber, the rub is they tend to use crap parts. If they use high quality valves you will really get raped. This job is not rocket science. Got to understand what is installed, how it works, how to remove it, have the replacement parts on hand to complete the job once you remove the old stuff.
Lot depends on is this your house or an apartment? Still when messing around with plumbing my first rule is
ALWAYS USE QUALITY PARTS. Junk and plumbing don't mix, you just go from the frying pan into the fire.
If you can do it yourself, you put the money into the top quality parts / tools instead of going into the next month's payment for the plumber's new Lexus. Nothing negative about plumbers here, they usually will get it done, probably earn their money. Jobs like these are just gravy for them, way, way overkill in the skills required. Beware of plumbers using cheap crap and charging for the good stuff.
Clean it up, lets make sure you really do have the type of valve I think it is. Make sure you have something like I showed above, maybe take a better pix once it is cleaned, post it here. Make sure you know how to shut off the water supply to the house / apartment. Then find some replacement parts. Ensure the flex braided tubes are of the proper length and connection types, they can be a bit too long, err on the side of being too long, don't try to get them exactly the length you measure.
Yeah, you should be able to handle this project. Do you know anybody to come hold your hand for the big day of surgery in the bath? Do the deed. Gets easier once you have done a few projects. Lets just make sure you know what / how.