Chances are the deck will push the 3.5s.
How many watts output continous (RMS) is it?
The 4x10s will be okay with the deck also if the output is good.
But, dont expect them to shake the car with their bass output. You might want to look at some 6x9s with adapting brackets to put in place of the 4x10s.
You have 5.25s in the doors? Concert sound setup? If thats the case, then I would suggest ditching the dash speakers and replacing the 5.25s with some nice 2 way speakers.
You cant run dash, door, and rear speakers all off of the JVC without some fancy wiring. The deck ideally should see 4 ohms at each speaker output. More ohms will sound bad and waste power. Less resistance will hurt the amp in the JVC.
Ask yourself...
What do you want from your system?
How much do you want to spend?
Do you want to replace it all at once, or piece by piece as you can afford to upgrade?
My suggestion is this:
Get some good 2way speakers for the doors, some 6x9s with adapters for the rear, and let the deck power it. However, in the future you can always add an amp to the system. If you are thinking about an amp, make sure your speakers will take a lot of watts continously and match your amps output with the ratings of the speakers.