I think it should be toki pona. Reasons:
semantically close words must share a common affix (not like biology and mathematics in English which are sciences but do not have the same suffix)
In toki pona, every science has a compound noun word beginning from sona. Biology is sona jan and Mathematics is sona nanpa. (Physics is sona lon and Linguistics is sona toki.)
This is due to the fact that toki pona has a limited vocabulary; so, to form words like "physics", it simply says the phrase "science of existence" or sona lon.
vocabulary must be finite and relatively small (a few hundred or thousand words would be fine) with no synonyms
The vocabulary is just 123 words. Almost all of these are polysemantic, there's nothing like synonyms.
grammar must be fully regular
Grammar is not fully regular, but that's only because of the fact that toki pona has a few words. However, there are not that many exceptions, as in any language like English or Spanish. I have studied 12 lessons of the official book and till then, the only irregularity is the fact that li doesn't follow mi and sina.
In all, the language satisfying (1) and (2) and partly (3) to its fullest is toki pona.
Another close competitor is Esperanto. It totally satisfies (2) and (3) and partly (1). (Some semantically similar words don't seem to have common affixes in them.)
So, in all, if you are looking for such a language, go definitely for toki pona or Esperanto.
PS. Even I felt the same (unable to successfully learn natural languages due to the several irregularities) and thus myself decided to go for toki pona first (because I already know a lot about it) and then Esperanto.