You don't say what kind of hybrid you have - some are designed for fast riding on roads, while others are geared more towards multi-purpose cycling, where their geometry is much closer to the old steel MTBs of twenty or thirty years ago. If your hybrid is essentially a flat bar road bike, then yes, maybe you probably do need an alternative, but if it's of the multipurpose type, then really, it should be more than capable to deal with the kind of terrain you mention.
The cheapest (and easiest) solution would be to stick some wider tyres on your hybrid if the rims (and forks) will take them - something like Schwalbe Land Cruisers, that are slick in the middle and a little knobbly at the edges. Those will give you good rolling on tarmac, grip off road, and the extra internal volume in the wider tyre will provide you with a bit of "boing" for the rougher stuff.
TBH, you really don't need any suspension other than that provided by the right tyres for countryside riding. I ride a lot of farm trails and gravel tracks out here in the fens, so plenty of ruts, pot holes, mud etc, though admittedly the roads aren't actually that much better! Anyways, for that, my bike-of-choice is a late 1990s steel Raleigh MTB, no suspension at all and with a short wheelbase, but fitted with modern components and the sort of tyres I've just mentioned. I did think about a hardtail, but really, it's just extra weight to drag around unnecessarily.
I do also have a hybrid btw, but that's set up for commuting / utility / bicycle away days.
Unless you're riding really gnarly stuff on a very regular basis, I'd keep your money in your pocket.