Log Analytics is just the service in Azure so there isn't a Log Analytics subscription. You just need to have an Azure subscription to use Log Analytics so that you can pay for whatever you use. You could use either a regular Azure Pay-As-You-Go subscription or an Azure Enterprise subscription. Then you would create the Log Analytics Workspace in your AIP tenant.
The E3 Licensing plan should be enough to access the audit logs, but the records are only retained for 90 days if you have a non-E5 license. If you have an E5 license they are retained for a year. I believe this rule still applies to the Preview feature but have reached out to the product team to confirm and will update this thread if anything has changed. For just accessing the logs I believe you should be good with the E3 license though. https://learn.microsoft.com/en-us/microsoft-365/compliance/search-the-audit-log-in-security-and-compliance?view=o365-worldwide
The AIP audit logs are also sent to the Microsoft 365 Activity Explorer, and to access that you need an E5 subscription.
https://azure.microsoft.com/en-us/pricing/purchase-options/pay-as-you-go/
If you want a full cost and licensing breakdown for your specific scenario, I would recommend reaching out to the billing team. https://azure.microsoft.com/en-us/support/options/
Here is the number for the sales team: 1-855-270-0615