Suggest index toolholder set please

Negative rake inserts need HP and rigidity to work the best, your machine should be able to use them to a point, but positive rake inserts work better and why they are usually recommended for hobby sized machines.

This document from Kennametal shows the different chip breakers for the negative and positive rake inserts. Negative rake inserts have straight sides and are used in tools that have a negative sloping seat so that the front side of the insert clears the work. This enables the insert to be double sided, so you have twice the cutting edges than a positive rake insert that only has cutting edges on one side. I use some negative rake inserts because I have them, but everything new I purchase is positive rake. As you can see from the table, there are a lot of choices depending on your cutting conditions. You don’t want an insert meant for roughing if you are taking finishing sized cuts.

David Best is a member here and wrote a book about the subject, it is available on Amazon I believe. If you do a search here, you should find some links to it. I don’t have it myself, but those that have purchased it speak highly of it.
 

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CCMT 31.51 and 31.52 inserts for that holder will cover most things. For aluminum 31.51 uncoated will work nicely. I've bought name brand inserts on down to the inexpensive ones direct from China in packs of 50 and for hobby use I just don't think it matters much unless you're working with difficult material or trying to maximize insert life. I tried some of the really cheap ones, found they worked well and then stocked up...at $1-2 an insert I don't worry if they don't last forever.
I am not finding 31.51 and 31.52 CCMT inserts. Did you perhaps mean 21.51 and 32.51?
 
Negative rake inserts need HP and rigidity to work the best, your machine should be able to use them to a point, but positive rake inserts work better and why they are usually recommended for hobby sized machines.

This document from Kennametal shows the different chip breakers for the negative and positive rake inserts. Negative rake inserts have straight sides and are used in tools that have a negative sloping seat so that the front side of the insert clears the work. This enables the insert to be double sided, so you have twice the cutting edges than a positive rake insert that only has cutting edges on one side. I use some negative rake inserts because I have them, but everything new I purchase is positive rake. As you can see from the table, there are a lot of choices depending on your cutting conditions. You don’t want an insert meant for roughing if you are taking finishing sized cuts.

David Best is a member here and wrote a book about the subject, it is available on Amazon I believe. If you do a search here, you should find some links to it. I don’t have it myself, but those that have purchased it speak highly of it.
That kennametal PDF is golden. It will take some time to assimilate it. Thank you
 
That kennametal PDF is golden. It will take some time to assimilate it. Thank you
You’re welcome, it is a great resource when deciding on what to buy. There is some great info in the tooling catalogs, the hard part is sifting through it all.
 
Ideally, the depth of cut should be equal to or grater than the tip radius.
 
I limited myself to 1/2 inch shanks as I was not certain that the 5/8 would squeeze into my BXA quick-change. @G-ManBart suggest that 5/8 will fit. Going to 5/8 would increase the diversity of mounting types. All the 1/2-inch stuff seems to be "S" or single screw mounts. Perhaps my next holder will be a 5/8".

Do you have BXA or AXA? 5/8" is standard sizing for BXA tool holders.
You can also get 3/4" XL BXA holders

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I am not finding 31.51 and 31.52 CCMT inserts. Did you perhaps mean 21.51 and 32.51?
Sorry...typo!

The inserts I meant to list were 32.51 and 32.52. 21.51 and 21.52 are the same shape, but a size smaller. I'll go back and edit that post and I'm going to reply to your question about positive/negative inserts separately.
 
I have BXA. I just discovered the XL version of the Share holder this AM. Thanks for posting it here

Looks like the XL version will work well with 5/8" shanks as it has 5/8 width, C, in the drawing. Thus it will fully support the shank.
 
I suggest you refrain from buying a "set" of indexable tools and buy 1 or 2 specific tools from a reputable brand like Sandvik, SECO, Kennametal, etc. I'll quote from my book on indexable tooling:

"Inexpensive, off-brand toolholders might be a reasonable way to learn and gain experience with insert tooling and even produce acceptable results. But the quality of these toolholders is inconsistent, varying from just functional to seriously defective. If you are just getting started and learning how to use insert tools, one sure way to quash enthusiasm is to start with a marginal quality toolholder.

If budget constraints restrict choices, my recommendation is to invest in one or two high-quality turning and facing toolholders from an established name-brand and learn with them. From there, you can add to the collection over time, as needs dictate, and as funds are available. This would be a far better strategy than starting off with a set of 5 or 10 off-brand tools of questionable long-term value."


I've send you a DM on this topic.
 
What a huge warren of options the is. Thank you all for your well considered responses. I'll admit that I took limited action prior to reading the last 3 posts. Here what I have done.

Settled on the trigon style insert and purchased one holder and a few inserts. A couple of different sites with detailed technical/comparative info indicate that the trigon is a good general purpose shape. I limited myself to 1/2 inch shanks as I was not certain that the 5/8 would squeeze into my BXA quick-change. @G-ManBart suggest that 5/8 will fit. Going to 5/8 would increase the diversity of mounting types. All the 1/2-inch stuff seems to be "S" or single screw mounts. Perhaps my next holder will be a 5/8".
So the holder I bought is SWLCR, standard facing from Mitsubishi with 1/2" shank
The carbide inserts are WNMG

So that gets one toe wet.

Links:
A Trigon insert is double-sided without any relief angle and thus must be mounted in a negative rake tool holder. As such, it is much more demanding of HP and creates substantially more tool pressure than an alternative tools/insert design that is mounted with a positive or neutral rake. IMO you'd be much better off starting with a tool holder that takes CCMT-style inserts such as the following:

 
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