RichardFX’s posts is very true. In addition to that, speakers are usually the part of the chain that make the biggest difference. And in the case of cars the cabinet also plays an important role as it usually really is mediocre at best. Luckily it’s relatively easy to make a big leap with a limited investment.
To start with the cabinet thing, get 3 self-adhesive dampening matts per door. Take of the plastic cover behind the door card. Maneuvre 2 matts through the inner part of the door, through the holes and stick them to the inside of the outer side of the door (I hope you understand what I mean, English is not my native language 
). Use the other matt for cutting up and covering up as many hole on the inner side of the door and maybe a bit on the plastic cover to reduce resonating (not sure anymore what I did but probably that). Now your “cabinet” has improved from very bad to sufficient (there still is room for improvement by using more matts but more work ánd more weight while there’s less improvement to be made). This will already make a huge improvement to the sound, particularly bass. Not so much as more but better in terms of quality.
As for speakers, I thorougly recommend switching to 8" speakers if you don’t already have that (I believe no Bose = no 8" but the weird 6x4" format). This greatly improves your choice for speakers. I have a set of Audison AP1 speakers and really love those. The only catch is you perhaps have to make some custom speaker rings for them (I did it with wood and some black paint). A bit of work but nothing too complicated. And otherwise there might be off the shelve speaker rings for MX5 NC’s.
And if you really don’t mind doing a bit extra, you could get a small class-d amplifier, there are many that do not require additional power wiring with a special ISO adapter.
The above is essentially my setup. Costed some time but not that much (really enjoyed it actually). And the sound in my car is now better than many factory optional systems that cost multiple times of what I have payed. And if you really want to spend as little time as possible on this, get a different head unit and better 6x4 speakers and be done with it.