By "unified" does that mean the chainrings are riveted on? But the crank arms are removable? I recently got a lightly used Shimano 48-38-28 crankset on ebay for $25. As long as the bb has square taper spindle you don't need to replace it unless it is shot. Definitely overhaul it now since you have to remove the crank arms anyway. I addition to the crank puller and crank bolt wrench (I got both in one from I believe Nashbar for either $12 or $15. Lifu brand. Works great.), you will need a bb hook spanner to remove the bb lockring. Spend a few bucks to get the Park with three "teeth" to engage the notches.
I assume the bike has 7 or fewer cogs in back. As long as that is the case, you don't really need to change anything but the crank.
Come to think of it, I have a similar crank, 170 mm, 48-38-28, low end Suntour if I remember correctly, that I took off my hybrid after just a few hundred miles. You can have it if you want it. Just send me an email where to send it. But you'll have to get your own tools and book on how to change it.
Regards,
Raymond