Difference between an https proxy and a VPN
In your example it is not possible to say whether the HTTPS protocol + Proxy has the same security level as a VPN. It really depends a lot on the specifics - i.e. which VPN software, what settings, etc.

However, in general you could say that it is possible to configure an SSL/TLS encrypted proxy and a VPN software to do the same kind of encryption with the same key sizes etc. so that they are "on level". 

When you visit a web site that is by itself encrypted (i.e. using SSL/TLS) many encrypted proxies works by essentially being a "man in the middle". Often this means that you install the proxy server's certificate as a trusted certificate in your operating system or browser, and all traffic from the web site is really decrypted on the proxy server and then re-encrypted for transmission to the client. This allows the operator of the proxy server to read all traffic in clear. Obviously this is a negative.

However some proxy servers work by essentially just passing the raw date to and from the same way a VPN would do - thus keeping the SSL/TLS encrypted connection to the website all the way from browser to web site.

So it depends a lot on the actual chosen proxy server software, its configuration, the circumstances, etc.

Your other question about whether to use free/cheap proxy or expensive VPN is also impossible to answer without knowing the specific. A free system might be really good, and an expensive system might be rubbish. It could also be the other way around.

In general the main difference is that it is easier to configure VPN to handle all traffic coming out from your PC - no matter the application or service. With proxy servers it is really on an application to application basis - so you risk "leaking" information that is not sent via the proxy server.