When Anders "VB-Killer" Hejlsberg left Borland/Embarcadero/whatever to work for Microsoft his first attempt to create a private clone of Sun's Java was released as Visual J++. This was designed to compile code for the related "private clone" Java Virtual Machine that Microsoft was distributing with IE and other products.
This was a big part of Sun's lawsuit against Microsoft, who lost. Part of the settlement was that Microsoft had to make efforts to prevent their private, incompatible JVM from being used anymore. Meanwhile A.H. went off to create another Java clone, but with enough lawyers looking it over to prevent another Sun lawsuit by avoiding making it too Java-like. This mess became C# and .Net, and VB got caught in the grinder as well which must still be cause for glee in some quarters.
When you install Visual Studio 6.0 (or parts of it) it tries to force A.H.'s rogue JVM onto your machine. As part of settlement compliance modern Windows detects this and raises an alarm. You can click through the "this crap won't be installed" dialog for the illicit JVM (just ok it). Some people will create an empty file named the same as the DLL that the VS 6.0 installation looks for and plop it into System32 before running the install. This prevents the warning dialog.
It is possible that installing a stand-alone VB6 SKU instead of a full VS6 SKU doesn't try to install the troublemaker. Or perhaps it does and this warning dialog is the one you are seeing about an "incomplete install?"
I haven't had to install VS6 recently, but I don't recall any other warnings. I've never tried installing stand-alone VB6 so I have no idea how that might behave differently. I can't imagine they'd act all that differntly though, because they needed that "phase 1"/reboot/"phase 2" in order to get some components installed properly on early versions of Windows.
Basically what you need to do is insert the first CD, then kill any autoplay installation attempt. Then go look at the CD with Explorer and run phase 1 of setup elevated (this means "run as administrator").
Once that completes it will probably reboot before you can stop it. Let it go.
When it starts to auto-run phase 2 you have to kill that. Then manually run the second phase elevated.
Once that completes you need to apply an elevation manifest to VB6.exe, or at least manually mark it "always run as administrator." VB6 was never meant to be used by a non-Administrator/non-Power User (and there are no Power Users anymore). This can wait until after you install SP6 though so you don't need to do it twice, but at least run VB6.exe a first time, elevated, before trying to install SP6.
Since the VS6 SP6 now comes in a 6b version with a 32-bit self-extractor/bootstrapper, installing it should be simple. Just be sure to start it elevated.
If you don't do this, parts of the install process don't get run elevated. This means they don't run properly. Some parts of the process do trigger "legacy installer detection" elevation or normal Windows Installer elevation - but by then you have a bit of a mess.
If things like elevation and manifests are strange to you... well a lot has changed since 1998 when VB6 came out. Some awareness is necessary to do successful development no matter what you program in.