"I want to see a Russian building."
I checked on your question. Some materials say が is used for physiological desires. That may be a little oversimplified, but in case you have not reached an advanced level yet, it is also a good way to remember first and you can revisit this issue later.
I have found an article for Japanese language teachers that explains about which particle to use in which case that will answer your question better. It is in Japanese though:
Both が and を are acceptable for the ～たい-forms of verbs. So you could say たてものを見たいです. There might be slight differences in what is emphasized depending on which one you use in some cases, but they should for the most part be interchangeable. I do believe が is more common though. It's definitely the one I use 99% of the time.
が is the correct particle to use with たい (same usage as with ほしい/すき/できる). を is actually a misuse. However it is a common misuse so Japanese decided to accept it as a correct particle too.
This 'の' is part of 'たてもの'. It is not particle here.
たてもの 建物 building ロシアの建物が見たいです。
Typical Duo style breakdown can be
[ロシア] [の] [たて] [も] [の] [が] [見たい] [です]