In a couple other responses you mentioned not having the tools for joinery. I think it may be beneficial if you tell us what tools you do have access to.
PVA is going to be one of the strongest wood adhesives you can find aside from construction adhesive and I wouldn’t trust any furniture only held together with glue.
Typically you are going to use the glue in conjunction with either joinery or metal fasteners.
Definitely go with pocket holes over dowels. Speaking from personal experience dowels are very hard to line up especially with a hand drill instead of a drill press.
I don’t know what your expectations for the desktop are, but with the tools you have at hand right now a rustic or farmhouse style desk would be the most reasonable expectation. Prepare to put in a lot of work and have small gaps between each board and a non-flat face.
To create a top that is perfectly flat and has no gaps is virtually impossible with the tools at your disposal.
If you truly want to build the desk yourself with the tools you have AND you need it to be perfectly flat you could do your absolute best to build it flat and tight and then place a glass top over the wood. Then you can admire working over something you built yourself and if you acquire the tools and skill in the future to make the top flat and fill the gaps you can refinish the wood and ditch the glass.
You may want to look into community woodshops or tool shares in your area. If available they will usually require you take a couple safety classes with their teachers so you know how to use all of the equipment and then a monthly fee for access to the tools and bench time.
Natural wood glues, general feedback?
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