I'm a self-taught hobbyist which translates to I make LOTS of mistakes, so take anything I advise with a bag of sand, not a grain.
I have 3 or 4 of the 5-piece set in your second picture, the RH one (second one over from the left) is my "go to" turning/facing tool. My first two sets came with regular Allen wrench metric screws - absolutely HATEd them. Very easy to round out the screws (or me over-torquing?). I think I bought the 3rd set from Shars or CDCO which came with metric torx head screws - huge improvement. I bought extra screws from Shars and replaced all of the Allen head with torx head. I don't know if the sets you're looking at have torx or allen, but if they're from Shars they probably have the torx bits. I don't think I've ever used the two intermediate tools, just the center, LH and RH.
There are lots of posts here regarding problems with parting. The first tool set gives you a grooving/cut-off tool which as mentioned above, if mounted securely in a QCTP, it will greatly ease parting. It also gives you an external threading tool, and probably all the turning tools you'd ever use. The set looks like part# 404-1052 or 1053 (1/2" or 5/8") from Shars for around $100.
The second set will require you to buy a number of different inserts: MGMN300 (parting/grooving), 16 ER AG60 (external threading) and WCMX 25.1 or .2, CCMT 21.5 and DCMT 21.5 for the turning/facing tools. By the way, I wouldn't buy the inserts from Shars unless you need them right away. You can shop on eBay and get the MGMN300 bits for under $12 for 10, but you'll have to wait a month to get them from China. Same for the other inserts, they are typically $25 or less for 10 of them from China.
Between the two sets (and since I'm spending you money . . .) I'd go with the second set of tool holders. You'll want to pick up a set of boring bars too.
That all being said, my dad was a high school shop teacher. I used to tag along with him after hours and in the summer when he worked in the shop making teaching aids, fixing equipment, etc. I recall "helping" him make visual aids for students out of 2 x 2's for grinding high speed steel. I painted the ground surfaces and stenciled on the angles and use of the bits. There's are pictures below of the text book pages showing HSS tools used in the shop. My dad taught 100's of students how to grind HSS and turn with HSS. Their high school shop never had any inserts in it. Didn't have any QCTP's either, just lantern style tool posts on Clausing 5400 and 5900 series lathes. Parting was usually done on a band saw since the lantern-style parting tools are extremely frustrating to use because of their lack of rigidity.
WOW, finally a summary. . . The carbide inserts are great for instant gratification and ease of use. You should learn at some point how to grind HSS bits, you never know when you'll have an odd ball job that requires a specially ground tool.
By the way, I believe the recommended turning speeds are doubled when you go with carbide over HSS. Google "Tom's Techniques" and watch Tom Griffin's videos on turning speeds; he's an excellent teacher. He recommends turning speeds of 400 divided by the work/tool diameter for steel which has worked well for me. That translates to 800 RPM's if turning a 1/2" steel round or drilling steel with a 1/2" drill bit/end mill ( 400 / .5). For carbide, the corresponding speeds would be 1600 RPM's.
Have fun tooling up, always fun to spend money on your shop!
Bruce
