Which one is worth buying? 03 Mazda RX-8, 04 Honda Integra DC5, 02 Toyota Celica, 99

A nice pick of cars there and all will be a good choice,different factors are there also like room wise IE the prelude,rx8,celica and quite small overall for rear passengers ,this might not be a big issue but a factor we have to look at when buying cars due to having young children on booster seats and boot space for kids bits,so if your mum wanted to take grandma out etc does she want to be pulling her out,but they are great cars also but a factor.
The Skyline ok iam on my second so i would say them but we have looked at the other cars before we pick one drove couple of them and tried the kids in them this was an issue why we did not also get my wife's dream car a mk4 Supra.
The Skyline we found ticked all the boxes it is very roomy front and back and offered a good boot/trunk space which we can get a monthly shop in,also being a 5 seater helped as it has a middle seat belt and room for the kids and an adult in between them.
Fuel wise i drive the turbo version so not the best on fuel but non turbo models are better on mpg on the 99 model you can go for the 1.0l and the 2.5l myself would go for the 2.5l version for that extra power and being rwd it is very very nippy and with hicas adds to great handling,
Auto wise both my skylines have been auto and offers instant power when needed when the pedal is down the car goes at full speed with rapid power and changes,a light touch and the car will change at low speeds and be nice and comfy to drive in town and slow driving.And the R34 gives the advantage of tiptronic box so you can drive auto or manually.
Reliability wise these are great cars and will not let you down with hardcore rb engines which are bullet proof.Parts wise there are plenty about and Nissan still stock parts down the early r32 models.
Overall great cars with headturning looks and a great iconic car which will not let you down.
Don't forget there is also a 4 door Skyline R34 version.
All you picked are great cars but worth picking of all the factors.

Also if you did go for the skyline make sure that insurance wise is rated for the non turbo and not the turbo versions.

I would buy the skyline for all of those except fuel economy, which still isn't that bad, and the prices of gas are going down. Overall its a great car. Definitely expect acceleration and handling.