Now that all the ground rules and the conditions have been stated, here are
my thoughts:

1. Your Dad's car, so definitely worth keeping around and doing it right.
My dad never owned a Corvette. Somehow keeping is '73 Impala isn't the same.
Long gone anyway, but I could have had it.

2. Your wife likes working on it - that right there says it all.

3. A bid of caution still applies from the original. My frame was quite
heavy in surface rust, like most street-driven cars, so I strip the frame
bare then had it sand-blasted. That was long before chasing stencils, paper
tags, chalk marks, and so on, so I wasn't doing anything out of the norm for
the time.  However, it did remove any chance of ever trying to find those.
If such information had been common knowledge then, it would have been well
worth a few days of cleaning with sponges, soap-and-water, and doing a lot
of photos at different angles to gleam anything that could be found.  Then I
would have sandblasted it, as the frame was perfectly clean afterwards.  In
other words, don't jump too fast into destruction stripping like media
blasting, sand blasting, paint stripping, etc. as there are many thing you
can find, photograph, and then go on to the stripping.

4. Without seeing it, you may be a candidate for minor restoration. It will
get you back together much faster without doing any damage to the car, your
pocket, or to the longevity. Frame off IMHO is much easier to work on,
however, much more intense. But you may be able to simply change out
bushings, u-joints, spot clean rust, and so on without stripping the frame
bare and blasting.  Then again, you see it, I don't, and you have to be the
judge.  Still, there is nothing like working on all clean parts.  As a
friend once say, you can completely take a car apart in 6 days, but it can
take you 6 years to get it all back together.

5. Paint, don't scrimp. You can take shortcuts everywhere but the paint
because it is the ONLY thing 95% of the people see and understand. You can
have a 100 pt car with bad paint but everyone will think the car stinks.

6. The Details - The ones readily visible, you might try to reproduce.  The
ones people need lifts and mirrors to see, do if you feel like it or if not
excessively expensive. Some of these stencil kits are like $50 or so.  You
can buy stencil numbers at Office Depot a whole lot cheaper. So are they
necessary?  Probably not.  Air cleaner stickers, radiator stickers, glove
box stickers, definitely.  Cheap, easy, and they are highly visible.

7. Original engine - real quandary.  The logical choice is to set it aside,
build a nice 350 to drive daily, and save the original. In practice, far too
many original engines get set aside to be "saved" and are never reinstalled
or even "lost" from the car forever.  Then again, if you want to retain the
original, and you lost a rod while driving it, it will make you wish you had
a 350 in the car and the original in the garage. 50/50 proposition on your
part.  Ideally, you could rebuild the original with all original parts and
have it complete and ready to bolt in  Then build a 350 with a basic
external appearance to stock Corvette. Most would never know seeing the car.
The engine being complete could be swapped back in the car in a day if
needed.  This way you have the original, you have the play toy, and you
don't have to worry. But see #9 below.

8. Interior - Original is the only way to go.  While many over the years
have installed other years, aftermarket, and customized the stock seats for
a better ride, these all stand out as unoriginal and it is amazing how many
"experts" will point this out to you like you are some idiot who doesn't
know you have unoriginal seats in there.  I had a midyear with flares
several years back  You'd be amazed of how many stopped me to tell me the
car was wrong. Like I didn't know.

9. Selling - while you may not intend to sell, one day you may have to.  I
never intend to sell mine but if something happened to my family where I
needed some cash fast, the car would be gone asap. A friend long ago left
his '61 to his family for his then 16 year old son. But since he was gone
and the family lost their bread winner, a few years later they sold the car
because of the need for money more than the need for the car.  Obviously,
the father wasn't around to "put the original engine back in" or "change the
seats back original" or a lot of other things people say they can do in a
day if they ever need to sell.  Fortunately for them, it was all together.
If you were ever gone or in such a situation, wouldn't you feel better if
you knew they got $35,000 instead of $25,000 out of it? (quite feasible in
orig. eng vs NOM situation)

10. All the right parts - fortunately, most of what you need is already
there, so this is a non-issue. But practicality comes in also. U-joints with
grease fittings last longer and are common $8 items at the local store than
the original '63 style at 2 or 3 times that price that have to be replaced
every 5 years.  Modern Goodyear, Yokohama, Goodrich, etc. tires rather than
nylon bias-ply reproduction tires. Fan belts from the local pars house
instead of dated, numbered reproduction items. Gas shocks instead of dated
gray Delco shocks that fail in two years.

Now that isn't to say you shouldn't buy those parts, because you can buy
belts, hoses, etc. and set them on the shelf for the day you decide to show
it only. and the prices on that stuff never goes down. Depends on your
available storage space and the extra dollars available.

11. You still have the date with Christie Brinkley right after she broke up
with Billy Joel. Don't blow it.  Of course, there are several ways you can
go about that date and still win.  It isn't a one-way-only proposition.

Good luck.