A few thoughts,
I've assisted with two people that have hearing issues, one guy in his late 60's that played guitar back in the day and a lady in her early 70's that had hearing damage from the flu as a kid. The guitarist had severe high frequency loss--over 50dB or so at 8K
He has hearing aids but does not like to use them when watching TV so--could I help. His mains were 10" two ways fully horn loaded which I rebuilt, designed a new crossover and installed an adjustable L-pad. The L-pad adjusted output over 800Hz. When at minimum, it was about +3dB hot and he could turn it up another +6dB if needed.
For him, the ability to manipulate both the level of the center, the voice processing, EQ and manual adjustment of the mid/high horn was critical. He picked up a Yamaha AVR with "clear voice" or whatever it's called--it boosts just the voices of the soundtrack and leaves everything else alone. The settings ended up +3dB hot for center level, clear voice on and boosted and the horn maxed out with the L-pad. He loves it and can hear it all so is very happy. Granted, it don't sound good to me but it was made specifically for him and he can go to concert mode with 103dB 1w/1m horn speakers and a 18" sub. Having a sub is great because he can adjust whatever bass he likes and it don't effect the deep male voices--season to taste.
The older lady did not want rock concert mode, likes bass but could not hear the TV speakers because of clarity. For her, the Yamaha sound projector sound bar and a Yamaha 10" sub seemed to be ideal. The sound bar has active 3.25" woofers and 8 little drivers as projectors. She adjusted the bass on the soundbar to what she likes (mid-bass and critical for deep male voices) then adjusted the 80Hz and below 10" sub that does the high 20's to 80Hz--to HER taste. The clear voice processing on and she went through all the EQ settings and selects different setting for movies and music.
Let her use it for a week to get use to it--left instructions how to change the adjustements and popped in to check. She had changed a few settings and told me it was the finest stereo she has ever had. Strangly enough, she throws in Bob Marley and kicks it up a bit so I can hear the changes. The mids were a bit hot but she must like bass because it was not weak.
First of all, I don't know what your hearing loss is, won't know your preference with hearing deep male voices, no idea what sub bass you require and no idea how you like your highs. Won't even try! I do have a bit of advice though, get an AVR (or soundbar) with vocal processing to raise the level of just the voices--that helps a lot. You might punch the center channel up a few dB so it becomes dominant--does not take a lot. If you want more highs, you and your wife should both agree on this--don't want it to be too piercing for her but not good enough for you. Make that adjustment together and you should find a happy medium.
A few bits on speakers--since you will be re-EQ'ing speakers--you might want to use some that have very stout tweeters and mids since those will be boosted. The other thing is to use speakers that use waveguides to limit the floor/ceiling bounce but allow wide dispersion across the couch. You can toe the left/right speakers in a bit and the waveguides will keep more sound from bouncing off the walls. The idea is to put the sound where you are and not bouncing off areas that you are not.
I generally don't recommend speakers and AVRs, but at a 600 dollar budget for AVR/sub and three speakers--off to Accessories for Less I go!
They start at $150 to $200 for the 5.1 channel versions so pick the one you like as long as it has voice or "vocal lift" processing.
Speakers next--three of them! Looking at ones with waveguides, the Yamaha's are sold out so...JBL Arena 120. A 5.5" woofer and a 1" dome tweeter in a waveguide should have enough durability to handle some spirited EQ. Here are a pair for $110.
Not sure if they have two pairs for that price so you can use three of them and go. If there is anyway possible, use three of them standing vertical to give you the best sound clarity for all three speakers. If you absolutely have to...they have a horizontal for center but it won't sound as clear.
Looking at subwoofers--because you need one mainly so you can adjust the bass to what YOU determine you like. It will also prevent deep bass from hammering the small bookshelf speakers so they won't distort to keep the sound clear. The Boston is on sale at $199 and should have plenty of punch to get your wife mad.
It goes down to 28Hz which is very good for a 10 inch sub and not too large I'd say.
Since I have no idea what speakers you will need be they 3 of the Arena 120 bookshelfs or a pair of the Arenas and the center...I'll throw the numbers out there.
Least expensive $150 AVR $220 used Arena 120 (two pairs used) Boston 10" sub $570
Center channel version $200 AVR used Arena 120 (one pair) Arena 125C center, Boston sub ... $690
The least expensive option is two pairs of the Arenas used and use three of them with a basic $150 AVR at $570. If you have to use a horizontal center, add $70 because it runs $180 by itself.
Generally, I don't recommend speakers but would specify a design to look at and offer at least three different companies that make that design. However, with a budget like that--the best is get a refurb AVR, get those Arena speakers used ($110 for a pair is almost theft) and it allows some flexibility with your setup. For clarity, I don't own any JBLs but they were chosen because of the stout 1" dome tweeter at that price point and the waveguide to assist with preventing floor/ceiling bounce. JBL does know how to make waveguides--no debate on that point!
My system does allow me to manipulate it when my inlaws drop in. They are 71 and have hearing damage from aircraft and a mild stroke. I turn on the "vocal lift" on my Yamaha AVR, bump it up a few pegs, boost the center channel by +3dB over the rest, turn down the surrounds, turn down the sub and will bump up the 1KHz point +2dB, the 2KHz +3dB and 4 and 8 KHz +4dB which they appreciate. My speakers use compression drivers and very large horns which can go louder than a THX theater from a simple AVR. No worries about any speaker damage when my father in law gets the remote. They love the clarity which is a good thing...I'm not getting any younger either! In another 20 years, I might need all those tricks myself and these speakers are keepers.
Good luck with whatever you decide, whatever you purchase--let us know and we can assist you in getting the best, cleanest and clear sound you can out of your system. Enjoy!