I think for a practice/learning game, it's definitely doable on your own without using Unity or another engine. Nothing in your description of your game is terribly complicated in and of itself, relatively speaking, other than the AI, which you'd have to code yourself, even if using an engine.
Realize that it's going to take longer to develop. But, if your goal is to learn, and not to simply finish a game, I think doing it without an engine is a fine choice and you'll certainly learn a lot in the process. On the other hand, if you're using an engine, you'll have more time to dedicate to gameplay mechanics, artwork, etc.
Both are valid routes I think. But, you'll get different things out of the process either way.
That said, and given your starting-from-scratch-ness, You'll want to do a few things first and you certainly have a few obstacles in your path. You'll need to choose a language. If you forgo an engine, you'll likely want to choose a library such as SFML, SDL, pygame, etc, depending on the language you choose. And, you'll need to become slightly proficient in your programming skills (even if using an engine). It will take time, to be sure, but it's certainly within your reach. And, it will be quicker using an engine.
This forum has tons and tons of resources though, and just searching through them, you'll likely be able to answer most of your questions, and if not, people are generally happy to answer a new one. The beginner FAQ will get you started on most of the things you need to do (language, libraries, engines, etc).
And, welcome :)