You have a number of options - I would suggest Sequester
You ask for the cheapest / most efficient method, but that is going to depend to a large extent on setting-specific knowledge we don't have. Even as a wizard of 9th level, there isn't much you can do by yourself to achieve this, but in most campaigns you would have accumulated sufficient treasure by that point to purchase the scrolls or casting services of others that would allow you to do so - provided such items or services are available in your game world, which we don't know. Another big unknown is whether this is something that will happen to your character by accident (such as finding themselves in the Feywild, as Treespawned suggests), even if you, the player, are working with the DM to this end, or is something that your character is intentionally seeking out.
At your current level, petrification
While petrified, you cease aging. Although the flesh to stone spell is sixth level and just out of your current reach, as Treespawned mentions several monsters have petrification as a special ability. Basilisks, for example, are a mere CR3 and should be something your 9th level wizard could encounter or even seek out if they existed in your world. On the other end you will need a greater restoration spell to be recovered. While this is only 5th level (and 100gp in materials), it is not on the wizard spell list, so not something you could do yourself in terms of pre-scribing a scroll and gifting it to one of your elven party members. However, if any of them are a bard, cleric, druid, or artificer, as well as certain subclasses, they should be able to restore you at 9th level - or pay for someone who can, again assuming such services are available.
You mentioned that "Something that would be likely to drive a person insane...is less [desirable]". A petrified creature "is unaware of its surroundings", but it is not, RAW, unconscious or unaware of its internal state or thoughts. Thus depending on how your DM rules, petrification could either be a maddening mental prison or a dreamless, timeless sleep. The consensus at Does a petrified creature stay conscious (and sane)? is that prolonged petrification is not prejudicial to one's mental state. However, if a petrified creature is still a creature, and is not explicitly unconscious, your DM might not agree.
With access to 6th level spells, Magic Jar
If you can get a scroll of magic jar and have 500gp for a vessel, you can separate your soul from your body. During the time your soul is in the jar, your body is in a "catatonic state". It is not clear whether your body ages during this time. If not, you need only make sure your body is protected as well as the vessel is. If your body does age regardless, you can cheat by possessing a succession of young bodies and living out their natural lifespans, returning to the jar each time you need a new host body.
This is, in fact, what the Master of the Desert Nomads did in the classic X4 / X5 adventure modules.
Of course, possessing another creature for its entire lifespan might be considered an evil act in your campaign, since as MindwinRememberMonica points out you are permanently removing their agency. Perhaps you can use the bodies of criminals that have been condemned to death, since their lives (and agencies?) are already forfeit, or the bodies of orphaned infants who have not yet developed a sense of self.
With access to 7th level spells, Plane Shift or Sequester
Why travel to the Feywild, where time might be slowed, when you can go to the Astral Plane, where biological time does not pass? According to the DMG (47),
Creatures on the Astral Plane don't age or suffer from hunger or thirst. For this reason, humanoids that live on the Astral Plane (such as the githyanki) establish outposts on other planes, often the Material Plane, so their children can grow to maturity.
With a single plane shift spell to get there, and another to return, you can spend the entirety of the timeskip on the Astral, conscious and active, but not aging.
Alternatively, with Sequester
If the target is a creature, it falls into a state of suspended animation. Time ceases to flow for it, and it doesn't grow older.
Since time ceases to flow, we explicitly don't have to worry about insanity induced from consciousness of the experience. Further, the spell can end on a trigger - such as, "When my party members call for me", which means you don't need to worry about having access to a spell to recover yourself later. If you know the specific date you wish the timeskip to end, you don't even have to rely on others to perform some action. And you certainly don't have to take morally-dubious actions like possessing others. For the safest, most complication-free experience, I would consider sequester to be your best option available at the lowest level possible.
With access to 9th level spells, you have many options
Astral projection sends your spirit to the astral plane, but keeps your left-behind body from aging.
Clone will provide you with a younger version of yourself.
True polymorph can turn you into an ageless form (like a warforged) or a race with a much longer lifespan.
Any version of imprisonment would result in:
While imprisoned, the target doesn’t need to breathe, eat, or drink, and it doesn’t age.
One of the five options, Slumber, explicitly makes you unconscious, if you are concerned about insanity.
However, when any version of the imprisonment spell is cast, you specify the trigger that ends it, but:
the DM must agree that it has a high likelihood of happening within the next decade.
Arguably, anything that you intend to reliably not occur for decades wouldn't also have a high likelihood of also occurring within the next decade, and thus planning such a long imprisonment in advance might not be permissible.
Wish might not be powerful enough to grant immortality without some major consequences, but "I wish to henceforth age at the rate of an elf" seems reasonable to this DM.