A try on your questions:

- should the ‘slimline’ models like the acoustic strat be considered or do they sound as thin as they look?
- jumbo shape? dreadnought shape?

It depends. You say you will play this mostly amplified. The sound is a combination of strings, pick, electronics, tpye of wood or plastic (Ovation), size of guitar. But you can colour the sound to your liking with additional electronics so it really doesn't matter. The major source of sound is the guitarist.


- what are the brands to look for in the gtr itself and in the electronics?

You don't need to look for brands but maybe you might need to avoid some brands -- at least for some models and years they produced them. If you would like to have some information on a certain brand or model use Google and search for musicians forums. Read several of them.


- what should I look out for in inspecting particular models in shops?

Do all strings sound on all frets or do they buzz? Maybe the neck is not straight or the frets are poorly adjusted.
Do you have influence on the action: Can you raise or lower the strings to your liking? For playing rhythm a higher action is preferred for playing lead, especially fast lead guitar, a lower action is preferred. Freddie Green playing rhythm guitar almost exlusively did have a distance of about 10 millimeters at the twelfth fret. Most guitars are sold with a distance of 2 to 4 millimeters at the twelfth fret.
Is the sound clear or dull? Does that change when you use the electronics?
When you testdrive it, play accoustically towards a mirrorlike surface so you hear the reflected sound. It is different than the sound you hear from behind the guitar.
How much slack is in the tuning pegs? The less the better.
Is there a zero fret at the nut or does the nut fix the strings to ring when played on empty strings? While a zero fret is not mandatory and not necessary in the first place it makes it easier to change stringsets that differ in gauge. The groove of the nut for each string must be wide enough for the string for easy tuning and narrow enough for good sound and the bottom edge of the stings must be at the same height. If you change to thinner or thicker strings you should also change the nut to match the new strings. A zero fret makes this somewhat easier: The grooves just fix the string on its position without any other task.

- is it true that round back gtrs (Ovation) can only be played by someone standing up?

No.

- does it really matter if the gtr is solid top or not?

Yes, if you have a particular vision of the sound the guitar should have.
Yes, if you want a certain response of your guitar.
No, for the average player.

- is it insane to buy a gtr direct (via internet) i.e. without inspecting/hearing the product before purchase?

See "my story" in my previous post. You might get disappointed or you might be positively surprised. If I have the choice I prefer to listen to the particular instrument not just to a look-alike. (They usually aren't sound-alikes or feel-alikes.)


If you have somebody you trust take this person with you as a type of emotion impediment. It might save you a lot of money and disappoiontment.



The above answers might not be complete but may serve as triggers.


Good luck.
Guido

Desktop; i7-2600k, 8 GB mem., Win 10 Pro, BIAB 2017; RB 2017 - latest build
Laptop: i5-2410M, 4 GB mem, Win 10 Pro, BIAB 2017; RB 2017 - latest build