A lot of stuff you can get online if it isn't available locally. The big box stores don't tend to carry very good equipment (especially lighting) unfortunately. I don't agree with the store owner about a larger enclosure being too much. The little guys tend to love running around and exploring (although they are all a bit different/unique). If they do appear to be timid or defensive then you can use a divider to make the tank feel smaller. If you get a large enclosure first then you can buy proper lighting once and save money in the long run. For now, I would at least get a 40g breeder size tank (about 36x18x18). Either one of the wide aquarium style ones from the pet store will work in a pinch, or something like the Exo Terra or Nat Geo front opening options. These aren't cheap though. I really like the Zen Habitats that Karrie has. They are a good size and construction. The front opening doors are really helpful for accessing the enclosure without having to disrupt the lighting. Given the cost difference between that and one of the glass front opening options I'd just get the larger tank right off the bat and keep it for good.
If you get one that is as large as a 40g breeder, go with a T5 fixture and bulb. This one comes with a T5 5.0 bulb included which is OK for about 6-8'' between bulb and main basking area. https://www.amazon.com/Zoo-Med-26053-Reptisun-Terrarium/dp/B00AQU8F2O You can upgrade the bulb (same fixture) to a 10.0 or Arcadia 12% https://www.reptilebasics.com/arcadia-desert-12-uvb/arcadia-d3-12-uvb-t5-bulb-22/ to bring the optimal range to around 12-14'' (10-12'' through a mesh top). These T5 bulbs last longer than the T8s in general. I get at least a year out of mine. I measure output with a solarmeter and in some cases have been able to get several years out of them (I don't recommend stretching this without measuring UVB output).
When I speak of basking area I think of it more like a zone. It's a zone that should be a diameter that is at least as big as the length of your dragon and provides a basking level temperature range and high UVB as if they are out on a branch or rock or fence post in the wild. To get a reading you can zip tie the temperature probe in the zone or nearby. I just zip tie mine to the basking log. Rubber bands work for this too. I would say since he is already laying on the branch to bask, I would make that the basking zone and get your readings there. You want temps around that zone to be in the 90s to allow a cooler place to hang out while still staying pretty warm, and the "cool zone" should be somewhere around 75-80(ish - these are rough estimates) to provide something closer to room temps.
If you get one that is as large as a 40g breeder, go with a T5 fixture and bulb. This one comes with a T5 5.0 bulb included which is OK for about 6-8'' between bulb and main basking area. https://www.amazon.com/Zoo-Med-26053-Reptisun-Terrarium/dp/B00AQU8F2O You can upgrade the bulb (same fixture) to a 10.0 or Arcadia 12% https://www.reptilebasics.com/arcadia-desert-12-uvb/arcadia-d3-12-uvb-t5-bulb-22/ to bring the optimal range to around 12-14'' (10-12'' through a mesh top). These T5 bulbs last longer than the T8s in general. I get at least a year out of mine. I measure output with a solarmeter and in some cases have been able to get several years out of them (I don't recommend stretching this without measuring UVB output).
When I speak of basking area I think of it more like a zone. It's a zone that should be a diameter that is at least as big as the length of your dragon and provides a basking level temperature range and high UVB as if they are out on a branch or rock or fence post in the wild. To get a reading you can zip tie the temperature probe in the zone or nearby. I just zip tie mine to the basking log. Rubber bands work for this too. I would say since he is already laying on the branch to bask, I would make that the basking zone and get your readings there. You want temps around that zone to be in the 90s to allow a cooler place to hang out while still staying pretty warm, and the "cool zone" should be somewhere around 75-80(ish - these are rough estimates) to provide something closer to room temps.