The only tools an inspector (B1 or B2) needs is his maglite, mirror, black biro and his stamp! LOL
No, seriously line maintenance and base maintenance certifying staff use their tools as required to do their tasks.. However as their mechanic, you will use your tools required to do the tasks delegated for you to do, unless they are the larger or type specific tools that the company SHOULD hold to fulfil the requirements of their PART 145 approval!!
"Yes" is the answer to your question. Line stations and MROs will have a minimum tooling list for engineers in most cases. Some of the european operators have their own supplied tool kits that are issued, but this ain't the case in the UK. Your tools will be your livehood, so its wise to get the best you can, especially the high use items!