I'll preface this by asking what sort of advice you're looking for - do you want to make your deck more powerful? More consistent? Faster? Resilient? Tuned for a specific meta? Or something else? I'll also inquire as to what your definition of budget is - based on your decklist, it looks to maxing out at around ~$2-$3/card.
Anyway, the two things I would first look for in a deck are card advantage and mana production. Running Ayara in the command zone gives you a significant benefit in this regard, since she provides card draw... but not card advantage, since you do need to keep her suitors flowing. I'll highly recommend
Swiftfoot Boots and/or
Lightning Greaves as a way to both protect her and grant haste - tap abilities work much better with haste. You could go a little deeper and also run some untap abilities like
Magewright's Stone, but I wouldn't do that without also having some other creatures with tap abilities worth repeating. you already have
Thornbite Staff, which is a solid start to that road - also interesting if you have something like
Avatar of Woe,
Visara the Dreadful, or
Whisper, Blood Liturgist.
Beyond your commander, I see ~8 sources of repeatable card advantage, plus a couple of one-off card draw effects. I think you look pretty good on that front. I'll throw out
Harvester of Souls as an option, but it is a bit expensive. The one thing I would suggest is token generation -
Pawn of Ulamog and
Open the Graves are both solid options for double-dipping on sacrifice triggers, and giving you more expendable bodies for Ayara.
After that, I'd take a look at mana production. I only see ~3 pieces of actual ramp, plus a couple of ways to fetch a land into hand. This doesn't seem like enough. Black doesn't have a ton of budget options for ramp (although it does have some very powerful mana doublers available -
Cabal Coffers,
Nirkana Revenant, etc). Because you're a monocolor deck, I think it's okay for you to have some number of colorless mana sources (even if they don't help cast your commander the first time) - I'll throw out
Charcoal Diamond,
Wayfarer's Bauble,
Mind Stone,
Worn Powerstone, and
Hedron Archive as options, but there are a ton of other options for artifact mana. Consider aiming for all the big black mana doublers over time though. I will call out
Cabal Stronghold as an easy inclusion though.
After that, I'd look at interaction. I don't see any board wipes - makes some sense, given how many creatures you have, but I'd still recommend running one or two. 41 creatures is.... a very high count.
Crux of Fate and
Deathbringer Regent are both cheap options, but better wraths do exist. Also no interaction for artifacts/enchantments - not that black has a lot of options, but I would recommend
Nevinyrral's Disk and
Steel Hellkite as potential solutions.
The last thing I would touch on is ways to close out a game, but I see
Twilight's Call and
Plague of Vermin (which looks hilarious, btw), which both seem like excellent ways to win with Ayara. Probably don't need anything else.
As for cuts.... as I mentioned, 41 creatures is a lot. I'd probably start by cutting some of the more low-impact ones.
Hope that helps!