I think the enclosure he is referring to is a vivarium, which is also what i have. It uses sliding glass doors on the front rather than a lid, so the lamps are secured on the inside of the vivarium, also increasing the risk of a skink touching it etc for burns, so if you observe him getting near to or touching the lamp i would suggest getting a guard, but in the mean time i would say it isnt necessary. Quite contrary to the types of enclosures that are typical in the US, mainly all enclosures, minus the glass exo terra terrariums are vivariums here in the UK. Its good that you got one, but if later on you decide to get a new one i would recommend a vivexotic EX48 if you cant find a viv that is custom taylored to the size you require.
This is what they look like, however they dont come with the decor lol.

The list i use for my skink is as follows:
- 42" UVB tube 10% or more (optional but many people reccommend, isnt necessary however if you supplement sufficiently)
- Starter ballast for the light
- Some form of heat bulb - i personally use ceramics as it allows me to maintain the temperature better, and is more efficient with night time temperatures, however heat lamps can be used and infra-reds can be used in the night.
- Thermostat - this will depend on the bulb you get, however with my ceramic i use a habistat pulse proportional 600w, with day/night function for automatic night time switchover
- Substrate - this is personal preference, however there are many strong reccommendations around and in the care sheet, i personally am using beech chips but am switching to a hemp substrate to eradicate the risk of impaction
- Water/food bowls - water bowl should be large in my opinion to let him get into and soak to aid shed/regulate body temps if needed, but also allows for a bit of humidity
- Hide and features - Hide is a must imo, and features are whatever you decide to put in there

You will probably already know this but its a good idea to stock on the disinfectants, in the UK there is a product range called F10, which many people support.
For supplements, i use nutrobal and komodo live food dust.