It is probably possible. It is the kind of thing where going through it as a beginner is likely going to take a long time and present some unexpected hurdles. It would be a good thing to do for someone who values self-reliance or learning about bikes or simply has a lot more time than money. If you do it I recommend enjoying the process and not worrying about how smoothly it goes or how long it takes. These sort of projects can easily go sour otherwise.
Googling around, the Raleigh Impulse appears to be a low-end 80s road bike. I couldn't find a 3-speed Giant Huron. Putting the wheel from it on to the Raleigh is almost certainly possible, but how complex of a job it would be depends on:
- What sort of shifter you're going to be transplanting along with it
- The spacing and chainline needs of the 3-speed hub in question
- Whether the gearing range you wind up with if you just use one of the chainrings already present on the Raleigh would work, even if the chainline it's currently sitting at would also be functional. (Taking the cranks from the Giant along with the hub would likely work better and have you buying the least stuff overall, but is a much bigger hassle and would need you to have the tools to take the Raleigh's cranks and bottom bracket off and put the Giant's on).
The Raleigh is almost certainly 120mm or 126mm in back. If the Giant is a more modern aluminum 3-speed, it's probably 135mm and wants a chainline of around 45mm. That might be around where the large ring position of the Raleigh lands, or it might not be. Also if these numbers are accurate, you'll be spreading the frame on the Raleigh. This isn't that difficult or technical but can be intimidating. You can do it accurately with a piece of string and a ruler to measure things and a long length of wood to do the bending. For dropout alignment, if the old wheel's axle is straight, you can cut it in half to make a dropout alignment tool, securing the halves on to each dropout with the axle hardware and bending the dropouts around after doing your rear triangle spreading and alignment until the dropouts are also aligned.
The commute distance you're talking about is considerable and so unless you get lucky, it is not a good idea to just run with whatever gearing you happen to land on if you use re-use the Raleigh's cranks. You can make it be whatever you want by buying a new 3-speed cog along with a chain, which are both very cheap. A basic chain tool is also cheap. Just transplanting the entire drivetrain from the Giant probably makes the most sense, and you could probably even take the chain along with it because those sort of bikes have essentially the longest chainstays that exist. You would still need a tool to shorten the chain. I'm assuming from its vintage that the Raleigh has horizontal dropouts; if that's not true you would need a way of tensioning the chain, which could probably do with the rear derailleur.
For the shifter, none of the sort of shifters that come on modern 3-speed bikes like the Giant really swap on to to drop bars in any kind of neat or straightforward way. If you were to willing to buy an older kind with a steel band type clamp, that could work. Otherwise you can just do it with the shifter it has and rely on finesse and tricks to not ruin the hub. One approach is measure the cable pull from each position on the shifter you've got and make marks on the Raleigh's friction shifter at the corresponding cable pull positions. All you need for that is a marker and a ruler. As long as it's close you won't hurt anything. Some people do a similar thing by feel or muscle memory.