Replacing water valves for bathroom sink
First, I don't think you'd have to change the valves. The photos don't show it well (and everything is very dirty), but the outlet connections are probably threaded and will accept appropriate hoses or compression fitting parts. Anyway, it won't hurt to replace them. 

You seem to have half-inch copper supplies and sweated (soldered) valve connections. The first valve you show should be correct. It has a compression fitting that mates to the copper supply once you cut the old valve off and clean up the pipe. A good alternative recommended in the comments is the new crop of push-on fittings, such as those from Sharkbite. When installed on properly prepared pipe they're considered reliable. 

You'll remove the nut and the tapered brass washer from the valve and slip those over the pipe. Slide the valve onto the pipe until it bottoms out, then bring the brass washer up to it. Thread the nut on and tighten it fairly snugly, but not crazy tight, keeping the valve all the way on the pipe. Be sure to support the valve so as to not apply force to the pipe. Use a wrench on the valve body and one on the nut. 

No tape or dope is required. The brass and copper deform to create the seal. This procedure is undoubtedly covered a thousand times on the web, so give it a search if you'd like more detail or a video. 

Now you'll simply install either smooth lines using the compression fitting or a washered supply hose to the valve output.