You can get a 256 MB VPS for around $2 per month from these guys - https://www.host1plus.com/vps-hosting/?utm_source=lowbox&utm_medium=link&utm_campaign=article - but bear in mind this is not going to be a high quality experience for that price!
Your budget is very low. It sounds like you are looking for a shared hosting plan and not a VPS. Anyhow, if you still find the VPS at such low rate, it will not have enough resources for smoother performance and most probably it will become worthless for your requirement.
When it comes to choosing a VPS, there are many things that need to be considered. One of the most important factors is the price. However, when it comes to cheap VPS, it can often be a waste of time and resources. Cheap VPS providers often offer subpar service and don't have the same level of security as more expensive options. Additionally, these providers may not have the bandwidth or storage capacity needed for advanced applications or websites. It's important to find a provider that offers quality service at a fair price so that you can save money and get the best possible experience from your VPS account.
Finding VPS hosting under $2 is quite a challenge. ARZ Host: This website aggregates deals on cheap VPS hosting, dedicated servers, and other hosting solutions. You might find some limited-time offers under $2, but be sure to check the specs and reviews before committing.
I do not recommend opting for a VPS within this budget. If you manage to find one, you will likely encounter various issues. Instead, I suggest utilizing shared hosting or cloud hosting, as you will likely achieve better results.