Ships & Modules

Still no reason to risk it, especially if it is an item with extreme value and people know that you are hauling it

As previously stated, the best ship to transport stuff like this is a ship with a covops cloak (EHP fit recons or T3's ideally, blockade runners are fairly conspicuous, have less EHP, and are more likely to be cargo scanned)

An even more safe option (depending on how good you are at lighting cynos) if youre going to lowsec is to simply jump a jump freighter directly from the trade hub undock to a lowsec system. While this obviously doesnt work in the return direction to a trade-hub, it does gaurantee invulnerability from gankers as long as you dont get bumped off your endpoint station.

I use a blockade runner.

Decent hold for modest size items. Align time and ability to fit a cov-ops cloak mean that they are pretty secure for both High sec and low sec use.
Fast warp speed means less time in flight so trips are faster too.

If you use the cloak often you shouldnt be able to be scanned except on undock. Using insta warp points on stations also reduces chance of being scanned.

Never lost one in over 2 years of use.

For high sec autopilot use a Drake rokh, or abbadon fit with a rolflamao buffer tank, scorpion works as well. For galente any of the Bs will work, the idea is to look like a mission runner headed out for whatever. Hide in plain sight. These are the cheap options, otherwise try a orca. For low sec anything that warps fast and can be fit with stabs will do the job.

Wont say something new but here are my advices for you:
a) High sec: Your first bet is a viator(or any blockade runner) with cov ops cloak. Fit meta 4 inertia modfiers on lows if you dont need the expanded cargohold.
Your second bet is an orca which can carry 40k in corp hangars. Thats unscannable and doesnt drop if she dies. The fit Keras gave(with 100mn mwd) is the best for trasports as it cuts the align time to 10 seconds from 50 seconds(warp, hit mwd and close it, when mwd goes off you enter warp)
For both cases you need insta undock bookmark for the station you use a lot as well as an insta dock one. Both reduces the time you spend near a station near to zero.
b)Low sec: Jump freighter is the safest(almost zero risk) hands down. If you want something cheaper for low volume you can go with viator or ceptor.

[Viator, Danger zone]
Local Hull Conversion Inertial Stabilizers I
Local Hull Conversion Inertial Stabilizers I
Expanded Cargohold II

ECM Burst II
10MN MicroWarpdrive I
Invulnerability Field II

Covert Ops Cloaking Device II

Medium Cargohold Optimization I
Medium Low Friction Nozzle Joints I

Has 5400 cargo, enouph for 2 frigates/1 cruiser packaged. You can change the expanded cargohold and the rig to something else if you dont want the space. ECM burst just in case. Tank isnt needed because agility is your best friend, thought an invu never hurts. Align time is at 3.7 seconds without mwd.

What sort of planning can get a carrier into high-sec?

Cloaky or nothing.

The only real way to be gank proof is to never be scanned for the gank in the first place =)

Ty, new to game, most helpful post on this topic thus far ^^

Just fit out a 100k ehp battle cruiser and you'll be fine

During my life in lo-sec doing PI simply tells me that nothing better then having a cloaky blockade runner and .....well ......a brain, even with a Badger I can still out run 90% of ganking (with some hairy moment) with an instant warp fit, in fact I am doing so good at it I only ever lost one Badger.

Freigthers, can take a beat and can move small stuff. Other than that, it requires skills.