Like PhilDW says there are many tools with the features you request. Here is a short summary of the pros and cons of a few of them: What installation product to use? InstallShield, WiX, Wise, Advanced Installer, etc. If you want to deal well with pre-requisites you would save a lot of time if you use one of the tools described in the link above. Using the "Microsoft Visual Studio 2015 Installer Project" type will likely fail. It has a very limited feature set.
WiX is free and open source, and contains a bootstrapper feature called "Burn". I have not used it recently, and I am not sure how "involved" it is to use, but here is the documentation for: How To: Install the .NET Framework Using Burn (first read the "Building Installation Package Bundles" instructions in "Step 1").
I have not used it, but several developers recommend the dotnetinstaller bootstrapper. Without knowing much about it, this is probably the easier option. Maybe give it a test spin.
You should be aware that a lot of Microsoft pre-requisites should come down via Windows Update these days, rather than be re-distributed by each setup - particularly the .NET runtime. This runtime adds a lot to the size of your installer (especially if it is small). You could offer it as a separate download on your download page (if you have one), or just tell the user to install it via Windows Update after exiting your setup with a launch condition.
Perhaps also check these answers:
UPDATE: Here is an answer with links to more samples on how to use Burn: Wix - How to run/install application without UI (towards the bottom - the github link to Fredriksen's project).
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