It is easy to load a model yourself, but then you have to animate it. that is far from easy, even from a full time professional. Skinning, animation blending, animation tree edition, skeleton retargeting.. it is all very common stuff but yet multi year project.
I don't recommend trying it, just go for Unity.
Using OpenGL directly to do a game is kind of a thing of the past.
I don't agree with you that it is a thing of the past it just depends where your interest level is and what you want to create. If you are in the habit of writing an engine and then a game you will hate unity as it is doing everything for you already, on the other hand if you just wish to make a game Unity is a great tool that can help you speed up that process.
Most games have their own format they read in and have specialised exporters for the modeling packages to build into that format or have an asset pipeline that compiles the asset into something the game/engine understands. The reasons behind having your own format is that most of the time the modeling packages store data in such a way that all operations are possible but it isn't fast to load this file. A game only cares about displaying the vertex information and maybe deforming this based on the animation system, however this data has to load extremely fast (TCR/TRC on the consoles say something like "you should be done loading within 60 seconds or so at maximum").
Modeling package data formats generally store their data as seperate arrays and use index arrays to construct the actual vertex streams to display form that during runtime (read lots of processing), a game however wants a data layout from which you can just instantly grab the stream of vertices and indices and dump them into a vertex/index buffer without any/minimal processing over the data.
