First, go nuts and spend $10/month since Kamailio does make a lot of database queries and who knows what else you may need to make modifications for and how much you'll want to store in memory before loading. I can tell you right now, using the LCR module properly will require more than a $5 VPS for the memory it will need to use.
Second, step back and ask "Do I really need a private network?". Not saying there is nothing against having it that way but do you really need it? Because you have to take into consideration a few things. 1) On the Vultr side, your Ethernet configs are now all manual. 2) You still need public access 3) If using Kamailio and done properly all your end points will source from one IP, Kamailios. So you expose the PBX to only that one IP.
Third, using a private network will require 100% that you need RTPProxy or RTPEngine running on Kamailio because you are actively going to need to update the SDP details each time SDP passes through Kamailio so that it goes from the public IP to the private IP and vice versa. If this isn't done or done properly, you will have No-Audio/One-Way Audio issues from the jump.
Fourth, Siremis is great but it is a database management and reporting GUI. It does allow you to issue some KAMCTL and other CLI commands from it but that's ALL it does. It does not create routing, rules or do any pre-generated programming configuration for you. It lets you add users and it generates the two needed ha1 and ha1b hashes but outside of that, it's just adding/editing/deleting stuff from the database.
You want Kamailio to process INVITEs from X IP/Domain differently than Y, you have to write the code yourself. You want to proxy one domain but do Location services for another domain, you have to write the code. Your routing selection, your failover handling, Presence, Subscribes, etc, etc, etc all of that has to be coded/written by you. There is nothing that is magically going to generate this stuff for you.
Oh this includes LOGS. You have to tell Kamailio what to log and when to log it. I actually spent hours on the logging process alone in my switches. But I also use cfg variables that can be adjusted realtime via the CLI to control that logging output. So I actually have a "SIP Debug" level that will show the SIP message in more depth. I have a "Firewall Debug" to show more of the SIP Firewall process.
Kamailio is something that can be setup quickly and very basically with little bells and whistles and work 100% but if you want real logging, routing logic, etc you'll need to block out some serious time to put this together.
Not to mention, depending on your end goal, you'll be making updates to FreePBX to make it work with the setup properly.