I finally used up all my ship slot, and I am debating whether to delete the old ships or buy new ones.

I currently have the following:
-Light cruiser
-Steamrunner
-Nova
-Heavy cruiser
-Defiant
-Patrol escort
-Ambassador retrofit
-Steamrunner retrofit
-The Type-8

I am planning to get the delta flyer and a carrier, and possibly the MVAE for the module to use on the Mirror Patrol

Good for you.

I don't see a question there, so not sure if you're asking for advice or just making a statement. If you have no available ship slots you could simply buy the 2 Ship Slot bundle from the C-Store for 500 zen.

You're not buying new slots for your new ships, you're literally buying them to keep the old ships. So consider and be honest to yourself: How likely is it you'll ever actually use that Miranda, tier 1 steamrunner, or other low level ship? Is keeping that option worth $5, or would you rather have more ships that you're likely to use on a regular basis?

Personally, I'd delete first. For example, drop the type-8 for the Delta Flyer. If for some reason you want the type-8 back, it's bought very cheaply for energy credits. Steamrunners can be reclaimed at the shipyard. There's three reclaimable slots right there.

Light cruiser, heavy cruiser, nova, and defiant (assuming tier 4 here) will set you back dilithium in various amounts to get back. This one comes back to the question: Is it worth $2.50 each to keep use of them as you accumulate more endgame ships?