I use Mobil 1 0W-40 changed every 5k miles along with a Fram Ultra (XG7317) changed every 10k miles in my three Miatas (91 and two 95s). You can get everything at Wallyworld whenever you need it, and my UOAs have always come out very well. First and second generation street driven Miatas are very easy on oil whether they're turbocharged or normally aspirated.
The turbo on my wife's 94 Miata was water cooled which no doubt helped keep oil temperatures reasonable, but I recommend you install some hood insulation above the turbo to avoid destroying the paint on the hood, The clear coat on my wife's Miata driver side hood was shot within a few months.
Good luck with the HLA clatter. I have had some success with Rotella T-6 changed at short intervals on another Miata. The clatter would go away after an oil change, and come back when the car needed another change several thousand miles later. Eventually, after 20k or 30k miles of regular maintenance combined with vigorous driving the clatter went away for good. None of my present Miatas clatter, but they've all used fully synthetic oil changed at regular intervals from early on.