1) There is no guaranteed method, but that budget might be better spent on links from news websites: two or three links at 1,500–2,000 rubles each. Yandex's crawler may notice your website and follow a link from a news site.
2) Try leaving links on jujuju.ru, but do not overdo it or spam.
3) Create an RSS widget in Yandex, install Yandex Metrica on the website and start visiting your site from the widget on Yandex's home page.
4) Try ordering page likes on Wmmail, where people will add three likes on VK, Twitter and Facebook for $0.03. Use these particular networks, but do not spend too much.
5) On https://news.yandex.ru, open My News and add your RSS feed there too.
6) Start adding unique news stories of more than 1,000 characters, ideally articles of around 2,000 characters, at 30-minute intervals. Aim for about 10 stories.
7) Visit them from Yandex as well, both from the home page and from https://news.yandex.ru/mynews). Make sure the visits are recorded in Metrica!