Ok, so the specs are something like:
- will work at voltages <50V
- mains will not be the main part of work
- work mainly done on breadboard, probably soldering some stuff
- gear should be decent and give reliable values, but nothing fancy/industrial professional grade
- space probably is limited in Japan, so size does matter
Thoughts:
- Enter the stuff with one decent multimeter, later stock up as you need more or better quality. Sometimes you need more than one DMM.
Tips: New stuff in the 50$ Range, like the mentioned zoyi model, or some equivalent Uni-T or Aneng stuff. That is ok to get your feet wet and is not too crappy to use later on. Alternatively some used Fluke handheld from ebay, if that is ok- like the 101 is great value if you do not have to measure Amps. Or, still smaller, some pocket DMM like [HIOKI] 3244-60 Card HiTester Pocket Digital Digital Multimeter- 40$ on ebay Japan as new product.
- Soldering Iron: This is a "one-shot" to get it right- and therefore it should fit. Hakko is nice, I have myself one. alternatively, if only small stuff gets soldered, she could go for a USB-powered iron like the pinecil oder some things like iFixit soldering station that gots reviewed by Dave:
The advantage here might be that it can be powered by an USB-C power supply- those could also be used (when bought at the right sizes and models) to power the rest of the gear, and/or use some frontend to a fixed voltage power supply like:
https://www.conrad.de/de/p/joy-it-jt-ps360-labornetzgeraet-einstellbar-0-60-v-0-6-a-schmale-bauform-3203105.html?hk=SEM&WT.mc_id=google_pla&utm_source=google&utm_medium=cpc&utm_campaign=DE+-+PMAX+-+Nonbrand+-+Learning&utm_id=20402606569&gad_source=1&gad_campaignid=20392975386&gclid=Cj0KCQjwlYHBBhD9ARIsALRu09pAZKNqNxL-94TDxR5i--YpiONoqxPsf2jCxVWG9BnifXSbkUcI-CMaAi-DEALw_wcB&refresh=true#productTechDataThose can be powered by standard cheap fixed voltage supplies, like notebook PSU etc. you might get cheap from ebay or recycle from defective notebooks.
-scope: Question is here, if the scope only has to check the quality of the signal, or if you have to do precision work- there are lots of el cheapo options available, or use an integrated multimeter/scope solution.
Those are also quite compact and should be sufficient to check for signals on Arduino etc. - no need to go for a full size scope like Rigol 1054 or so.