What is the best software to use for website lifecycle and action trigger based emails?

I can't say what is 'best' but can suggest Criteo as a reputable specialist in this area.

This would really depend on the vertical of your company and the CMS you use. IE are you E-Commerce? Are you using a platform like Magento or Shopify, and if not E-Commerce, something like Wordpress?

This is important both from an feature set integration and economic standpoint. You'll want to find the provider that best integrates with your CMS to maximize its use cases and minimize costly custom development.

A few leading providers are:

Klaviyo, Bronto, Listrak

Depends on your budget, but for most, it's Hubspot. Infusionsoft and Marketo are pricier options.

There is not perfect solution. I only use Infusionsoft for my customers. I understand that there are other solutions, but for automatically self-segmenting your prospects as they drive through the sales process...there is non-better for the price.

There are softwares you can use but they have specific functions. For example, for drip emails you can use, Drip, Sendloop, Customer.io, BombBomb, Vision6, Quickmail, Vero, ConvertKit, Gumroad, and Knowtify. For marketing automaton, you can use Contactually, AgileCRM, HubSpot, Infusionsoft, Interakt, Intercom, Jumplead, Hatchbuck, and LeadSimple.
Besides if you do have any questions give me a call: https://clarity.fm/joy-brotonath