I have seen the future.

This is a breakdown on getting Insubstantial characters to interact with physical things. It's ordered in roughly order of cost of the enhancement(s).

Partial Change, +20% only

You may interact physically with substantial targets, but do so by materializing parts of your body to do so. This renders you vulnerable to Parry/Block, and various kinds of counter-attack (Wait-and-Attack will probably become very popular for your targets). Does not require Affects Substantial, as you are exposing yourself. Your entire hand (or foot, or whatever) becomes substantial as part of any attack.
If you want to attack while insubstantial and be immune to counter-attack by remaining insubstantial, you should take Affects Substantial and add the +40% Affects Substantial enhancement to your ST.
You may only interact by pushing, shoving, hitting, poking, etc. You cannot lift or pull things, nor can you grapple or pin. You may not use extraordinary abilities without taking Affects Substantial - you may only interact crudely; even extraordinary abilities tied to body-parts (the Deathtouch spell, an Innate Attack with the Melee limitation defined as claws, etc) cannot be used without Affects Substantial applied to Insubstantial (and to the extraordinary ability, if appropriate).

Partial Change, +20% + Can Cary Objects, any level

As above, but you may now also lift and carry, pull, grapple, and pin (subject to your Can Cary Objects weight limit). Objects remain substantial, and the body part(s) manipulating the object are also substantial (and targetable in combat by substantial foes).

Can Cary Objects, any level

You may turn objects insubstantial by holding/wearing them when you become insubstantial. When you drop them, they become substantial. You can't throw them or swing them as weapons or use them to manipulate physical objects (unless it's a magic ghost weapon Gadget type thing, which is cheating 😁 ). You may not pick up substantial objects while insubstantial, nor may you turn substantial objects insubstantial without carrying them with you as you yourself turn insubstantial. To acquire more insubstantial objects, become substantial and then pick them up like normal people.
Despite lacking "direct" combat actions, this enhancement still has significant combat applications - pulling the pin on a hand-grenade and dropping it (so it becomes substantial and harmless to you) is only the most flashy. It also allows you to do things like drop caltrops, blow poison powders or smoke/gas issuing devices, and generally deploy environmental hazards.

Partial Change, +100% + Can Cary Objects, any level

You may now also take your equipment that became Insubstantial with you, and turn it Substantial, without dropping it. This allows, eg, a Super-Ninja to walk through the wall with his trademarked poisoned shuriken and throw them or use them to claw at guards, rather than just dropping them - which isn't very ninja-awesome. It's not specified in the quote, but it seems very much that it goes the other way as well - you can steal things and turn them insubstantial.

Affects Substantial, +100%

If you have any ability that notes it can be used while Insubstantial on substantial targets, you must take this enhancement. This includes abilities that work with a penalty when crossing states. This also includes any ability that has the Affects Substantial, +40% modifier applied to it to upgrade it - yes, you have to pay in two places. It's that expensive because it's that awesome.
Failing to take this enhancement locks out all abilities that would normally otherwise cross the substantial/insubstantial border to work only on targets in the same condition as yourself .

Affects Substantial, +40% applied to ST

As per GURPS Power Ups 4: Enhancements pp. 9-10, following the provided procedure to "Enhance" ST with Affects Substantial benefits all unarmed melee attacks, for striking only. Remember Claws, ST-Based Innate Attacks, Strikers, and Teeth will also require the enhancement if you wish to enjoy this enhancement with them.

Untouchable Deadly Assassin (Contains House Rules)

An Insubstantial character who wishes to be able to interact with the physical world as if solid, but be interacted with as if Insubstantial without any of the pesky problems of partial materialization should take the following meta-enhancement on Insubstantial:
Untouchable Deadly Assassin (+350%): Affects Substantial, +100%; Can Cary Objects: Heavy, +100%; Cosmic: Interact Physically While Completely Insubstantial, +50%; Partial Materialization, +100%.

Cosmic: Interact Physically While Completely Insubstantial

This is an application of Cosmic: Removes Restrictions. This house-rule modifier requires every other enhancement in the meta-enhancement; it is not separable. Can Cary Objects allows supporting weight; Partial Materialization gives the ability to manipulate physical objects while otherwise Insubstantial; Cosmic is required to remove the requirement to partially expose yourself to attack, and Affects Substantial is required because you now have an ability that allows you to interact physically with the environment while remaining safely insubstantial.
You will still need to apply the Affects Substantial enhancement to any extraordinary abilities that you wish to also apply to the physical world.
Note that defenders aware of your attacks will still be able to defend. You will need to add separate enhancements to your abilities to bypass this. Being an Untouchable Unstoppable Deadly Assassin is terribly expensive. Go shopping in the Malediction and Cosmic section for the usual heavy-hitters in this respect, but Respiratory, Blood-Based etc may be useful.
Note to GMs: You may wish to also require the player to buy Affects Substantial on ST as the character is now effectively enjoying the complete benefit of this enhancement.