Welcome Samuel, that looks like a decent car to start with there! I love the convertible's also, so cheers to you on that one.
My first 2 thoughts for anyone looking to upgrade these old vehicles is:
1. How much are you willing to spend overall? What is the budget and over what time?
2. Intended use of the car.
Those 2 things can guide you to buying the right parts and to prevent you from going too big or too deep in one area. (like engine, or paint, or suspension)
Almost all of these older cars are going to need new springs,...or a conversion to air-suspension but the latter can get involved and pricey.
So, I assume you'll need to lay out a few hundred dollars on new springs. The folks at Eaton can help you pick the right set based upon your vehicles options (like A/C, big block, small block, aftermarket alum. heads, etc) or you can buy a set straight from a number of companies like Hotchkis, Global West or Year One and Classic Industries.
You'll want new shocks of course - standard HD type shocks are probably fine IMO.
Don't overlook good tires! An upgraded suspension on 7-10yr old tires is crap.
The next item will cause you to think a bit. Do you want rubber or polyurethane bushings? Poly lasts much, much longer but it is firmer, and can tend to feel harsh to some. (same decision for front or back suspension)
Part of the decision above, is to also ask how much you can spend. A handful of places are ready to sell you 'plug and play' parts! New A-arms, or rear control arms....ready to go, just bolt them in! The alternative is to attempt removing and installing the bushings on your parts yourself. (I would dare call that highly time consuming for a family man with moderate skills working in a typical home garage.
After you've answered that - you can look at the budget to decide if you want to spring for new front/rear swaybars. They will make it corner better, but with a car weighing 4000lbs +, of course it will probably never be chasing Porches.
Addco is a good place for swaybars.
Wheels/Tires. for the old look, a lot of people go with the 15" front and rear with anywhere from 225 - 255 up front, and 235 - 275 in the back. Depends upon what look you want to go for. (similar to the springs....Stock look?, or sitting lower?)
I was assuming your car probably had power disc brakes already, right? Your post above makes me wonder if yours has drums all around.
Some good quality rotors and ceramic pads on the front, new drum pads, maybe a drum in the back and you may be good to go, assuming everything else is in working order. Just take the time to visually look at every inch of brake line from front to back. If it looks rusty or deteriorated, you should get a new line. "Right Stuff' and other places sell those.
I think the 68-78 Vette spindles work too. Be aware that some brake kits using your stock drum spindles. A few on here report happiness with 'getdiscbrakes.com'. It's a bit dizzying all the vendors in that space, I'm finding it difficult to separate the wheat from the chaffe.
I agree with the others about the Vert top, finding a skilled shop to do it is key. It won't be cheap either.
You'll want to decide up front whether you go with Vinyl/stock material or the less-shiney 'cloth' type which does cost a bit more. I chose cloth for my top.