There's a thread regarding C# game engines (started yesterday).
You must be seriously, seriously pro to plan build an engine. There's no chance to do something serious without getting more experience first. Of course, as there's no definition of what exactly an "engine" is, you could cut a lot of corners and claim to have an "engine": that's not how it is supposed to work.
Game engines, no matter what they tell you, are not fun.

If you have to ask how to build an engine you're definitely not ready to build one
Building an engine is absolutely not a beginner's job, so it'd be best to put that idea on the shelf for some time until you're ready for it

Mostly in game engines there isn't a fixed point on where to begin, you could start off anywhere and build gradually on top of that. The easiest would of course be to lay out a design for your engine and start with the system that has the least, or preferrably no dependencies on other engine systems.
From then on it just comes down to implementing the systems you designed, you need to have a clear vision of what the engine is supposed to do, how it's supposed to do it, and for which goals it's going to be used. Writing an engine without having a clear usage goal in mind is substantially harder. This of course all has to happen within the limits of the system(s) you'll be targetting.

Building the systems themselves will be all up to you, and to build an efficient rendering system or audio system (for example) you'll be digging deep into the gritty details of how such systems work, and you'll need to be quite familiar with those details if you want to build something that actually works, and works well.

Let me give you one piece of advice: If it's games you want to build you should just pick an existing engine and build the games you want. The chance of your custom-built engine outperforming any of the available options will be quite minimal. If you're actually interested in building engines you should first of all consider whether you actually have the required skillset to start one. I'll have to disagree with Krohm here, because building engines can be fun IMO, but it's completely different from building games, and if you don't have a clue as to what it takes to build an engine you'll get frustrated quite easily, and the development process overall will not be a fun ride.

In the end nobody can stop you from building one, but don't expect there to be an abundance of tutorials or guides on the subject, it will all have to come from yourself

I'm sorry to say but two university assignments isn't be enough to make an engine. I made several games from scratch (without using engines) and several other applications (all outside the university) and I still don't think I would even consider making my own game engine. A game engine is not about games. It's about architecture, software engineering and all the stuff that is not really game related (or at least not only game related).

So head the others' advice and make games instead of an engine, or get pretty damn solid knowledge and experience in software engineering (probably several years of intensive programming)

Hey there - I'm in a similar position, and I'm going the game-engine building route for the following reasons:
a) Building up a knowledge of how game engines are structured is important to me. Building even a simple pac-man game engine myself would, for me, be enjoyable! Sure, it will be frustrating - having to write boiler plate code myself, but that's part of the experience for me. It's a richer learning experience in my view.
b) Using ready-made game engines, whilst yeilding much more immediate results, teaches you less about the princples - I think.

So basically as you've probably concluded, knocking out as many games as possible is not my objective. It all depends what you enjoy. It doesn't bother me that everything I'll do has been done before many times - that's not the point. The experience is of more importance than the tangible results for me.

In the future maybe I'll use ready-made game engines - who knows. Not yet though.

And what principles would building a game engine teach you, you think? I don't think building an engine is a great learning excercise, because it requires you to already know all there is to it to actually get something up and running. If you start out with the idea "I'll learn everything while developing" you'll likely end up with a horrible mess of barely functional (or not even functional) code.
There is a common misconception (IMO) among beginning developers who think that building an engine will somehow give them much more experience than building games will, and that they'll learn so much more by throwing themselves onto an engine project from the start instead of actually gaining the skills required to build an engine.

But then again, nobody's stopping you from attempting to build one, but please do keep the advice given to you in mind

Hey there - I'm in a similar position, and I'm going the game-engine building route for the following reasons:
a) Building up a knowledge of how game engines are structured is important to me. Building even a simple pac-man game engine myself would, for me, be enjoyable! Sure, it will be frustrating - having to write boiler plate code myself, but that's part of the experience for me. It's a richer learning experience in my view.
b) Using ready-made game engines, whilst yeilding much more immediate results, teaches you less about the princples - I think.

So basically as you've probably concluded, knocking out as many games as possible is not my objective. It all depends what you enjoy. It doesn't bother me that everything I'll do has been done before many times - that's not the point. The experience is of more importance than the tangible results for me.

In the future maybe I'll use ready-made game engines - who knows. Not yet though.

You confuse from-scratch coding with engines. Pac Man requires nothing like an engine. Even a fist person shooter doesn't require an engine. Engine is something for making more games than one. It's not only some reusable code, it's the whole toolchain required to make more games (okay, definitions may vary), and usually implemented in a way, that it's commercially releasable or at least usable by more developers (or a development team, ie "in house" engine) in a structured environment.

You are talking about from-scratch coding, with is fine, I did/do that too, but that's light-years form engine programming.
And another thing, using engines does teach you principles. If you haven't ever used an engine and finished/polished a game (or several), I'm sure you won't be able to make anything that resembles an engine (even if you make games from scratch)