Thought I'd deliver a minority report - get yourself some straps!
I worried a lot about grip strength when I started deadlifting, which in retrospect I wish I hadn't. I did a bunch of grip training, and the only outcome was a persisting elbow tendonitis. Since my grip was my weak point, that was what was worked the hardest during deadlifts, so the extra grip work ended up being excessive volume that my poor arms couldn't handle.
One of the things I've since realized is that it wasn't my grip strength that failed me, it was my grip endurance - it wasn't my 1RM lifts where my grip failed me, it was during high-rep work. And while I do care a lot about being able to set my new personal bests strapless, I don't see any reason why I shouldn't use straps for the volume sets, should I feel the need.
My priority list would be something like this:
- Keep on deadlifting. It's great grip training, and it's specific training for your current goal, namely deadlifting. (I'm not so sure about the carryover from, say, grippers or plate pinch to deadlift, though.)
- Chalk. It does a world of difference for deadlifts, and has benefits for most other lifts. (Liquid chalk is fine, perhaps not quite as good as chalk blocks but much more convenient.)
- Mixed or hook grip. You can use overhand for lighter sets, but this is just such a game changer for heavy lifts.
- Straps. Use them when you need, and skip them when you don't. To me, I skip them during heavy, low-rep sets, but the more reps, the more I'll consider them.
Straps are great. No, really! They take up next to no space in your gym bag, even the good ones aren't particularly expensive, and they last more or less forever (the textile ones do, anyway, leather dries out), and they are great help to get in volume. They also spare the skin in your hands if you're doing a lot of deadlifts, which neither hook/mixed grip or chalk do.
Anecdotally, I would even say that the negative effect on grip strength by straps is somewhat debatable (you still use your grip, you know). I used straps for pretty much every pulling exercise for over 6 months (because tendonitis), and when I finally decided to try lifting without them, I could keep on using the same weight for my deadlifts (which had increased by at least 20 kg during my straps-only halfyear).
I'd also say that grip strength is one of those things you worry about as a beginner. I'm not sure why the issue disappears, but I'd guess chalk + not using overhand grip explains a lot.
Finally, if you think straps are for wimps, go tell the World's Strongest Man contestants.