Numenera is a game that is fairly resistant to the effects of party imbalance, so it isn't too much of a problem once your players realize that experience spent on short-term benefits can mean the difference between life and death (or at least unconsciousness), and you realize that setting difficult encounters can sometimes be a good thing.
You will learn how best to balance combat for your party as you go, and while some combats should be a breeze and others are challenging but not overly difficult, others should be difficult to the point where they do have the potential to lose, and short-term experience spending may be (part of) the key to winning. (On a similar note, this is also important for promoting the use of cyphers and artifacts because your players will more than likely begin the game hoarding them like treasure).
If you still feel the need to house-rule experience expenditure after playing for a while, solution 1 is the better of your two ideas, and has been put forward by Monte Cook himself as an optional way of handling experience in the Numenera Design Diaries (under the section Using XP - fourth paragraph). The only real disadvantage to this system is that it does limit the way your players can spend their experience, but it also makes the decision of whether to spend that last point of short-term experience that much more critical.
Your second idea would require you to halve the experience you give out since each point would be used twice. Your players may also spends their experience on short-term benefits they don't need just so they can push the experience to the long-term pool to be used on character advancement all the sooner.
Note in advance that there is no published reference to exactly how this should be treated (that I can find) - this is based purely on the otherwise published intent of the experience system of the game (and how I interpret it). Also note that the Numenera core rulebook as written does feature many ambiguous and seemingly unpolished rules, so are often open to different interpretations.
Discovery, not possession, leads to advancement
The core of Numenera's experience system is the idea that discovery leads to character advancement, thus finding artifacts, discovering secrets of past worlds, and similar forms of increasing knowledge leads to character advancement (as detailed on pages 108-109).
In comparison a player crafting a specific artifact of their own devising is not discovering something new, they are expending effort to create an item that they have considered and planned before beginning the creation process.
Discovery is also something that requires considerable time and toil from the players - just as they should not be awarded experience for walking into the nearest store and buying an artifact, they also should not be awarded experience for something they can do from the safety of a workshop.
Even for significantly powerful items that may require adventuring to obtain rare components, there may be some experience gain in the process, but the item itself is the reward the players are seeking, thus they should not directly gain experience from the creation of the artifact.
XP for nothing
Consider also how broken it would be for a player to craft a level 1 artifact of their own design, and everyone in the party thus gains 1XP. As stated on page 109 PCs gain a minimum of 1XP each for discovering an artifact, thus a level 1 artifact is still worth 1XP each (although the same section states to round down if necessary, so depending on your interpretation 3 players may earn nothing from discovering level 1 & 2 artifacts). Either way this would still become a very cheap form of advancement, but creates an otherwise bad gaming experience without the GM taking action to stop it.
Best Answer
In Numenera practically everything has a level, but there is no such thing as an item level as opposed to a cypher level - a cypher, like a door, like a lock, like an NPC, just has a single level associated with it which is a measure of its power, ability, resilience, what it takes to craft with it, and just about anything else that would require a roll or comparison with an existing value.
Just like a door the level of the cypher indicates the target number required to break it - it is not based on a separate level determined by the material from which the cypher is made.
Note that rolls to find and identify cyphers are not dictated by their level, and have separate rules on page 280 of the Numenera rulebook.
Also for the purposes of crafting, the level of all numenera items should be increased by 5.