Java web hosting advice

Hi.

I've been on quite a journey over the years finding a web host that supports Java and allows you to have the typical things like cPanel, email, PostgreSQL, and ssh support. It seems that the time may be upon me to move to a new plan or host. If anyone has any advice, that would be great.

By "supports Java", I mean allowing me to run my own private servlet container or app server. I don't care about JSP support. I don't use JSP's. I don't want to be stuck with some ancient or older version of Java either, such as JDK 1.3 (yes, you read right) up to JDK 1.6.

I've had a private Tomcat hosting plan with Arvixe, but I was recently informed that they no loner support Tomcat and that I'll have to administer my own Tomcat. I'm fine with administering my own Tomcat. I replaced their provided Tomcat 5.5 with Tomcat 7 and then eventually TomEE 1.7.x and have been administering it just fine for the past few years. Still, there's remaining questions of "what the heck am I paying for then?" and technical questions such as "If I can set my own heap size, then what's the limit?" (I don't need that last question answered, Reddit). I think Arvixe has been awesome so far. Their support has been helpful, responsive, and friendly. They've let me run on Java 7 and my own TomEE.

Couple all that with not having 99% uptime, my patience is finally at the point where I think I need to start considering other options. I'd consider VPS, because it seems like I'd be allowed to run anything I want within the HD and RAM constraints. I've also heard a lot about AWS or Heroku, but I don't know if they offer you your own mail server and PostgreSQL db (which is critical). I don't know much about those services. I'm also looking for something that's cheap. Ultimately, this is for a personal business.

What do you recommend?