A shirt is a good place to start, yes! I'd suggest probably not doing a hand sewn expensive linen one on the first try, because it would be very disappointing if after all that work it didn't fit or you weren't quite happy with the construction. Oh, that reminds me, I need to update that shirt post with the better gather sewing technique I didn't know about until recently.
A simple collarless waistcoat is also a good project, and I really like 1770's-early 80's ones for everyday wear. My Werther's waistcoat video is currently the most thorough explanation I have of the construction, which is overall pretty simple - lined front and unlined coarse linen back, and easy to adjust before you finish the seams to make sure it fits just right.
My 1730's waistcoat post is a bit more complicated and has a lot of progress pictures.
Here's a link to my list of 18th century menswear resources, which I keep meaning to organize into a proper blog post someday. Oh heck, I need to update that too, it doesn't have my button tutorial videos.
And about embroidered waistcoats, remember that they don't need to be hugely complicated! There are plenty of late 18th century examples with only a little bit of embroidery! (Which is another thing I've been meaning to make a post of...) Here's a link to my extremely bloated pinterest board of 18th century waistcoats.