Monster Hunter 4 Ultimate (3DS-Citra) or Monster Hunter Generations Ultimate (Switch - Ryujinx LDN build so you can play multiplayer). Generations Ultimate is a switch port of a formerly Japan-only 3DS game (MHGU is the English release) so if you're worried about emulated Switch performance it's one of the easiest to run games on that console.
MH4U is probably the best way to play the fully realized vision of the oldschool formula (mechanically it's "complete" in this game) and MHGU allows you to to either play with MH4U mechanics (Guild style in game) or with various twists (Valor, Adept, Alchemy styles) which radically alter the combat style of each weapon. I played through the game first in Guild style (because I didn't speak Japanese and only had that version at first until the international release) and while the game is completely beatable never using any weapon styles/hunter arts, the post-game content (Deviant monsters) are absolutely designed for you to use those things.
If you had to make me just make a gut call on what to try- I'd say MH4U.
If playing MH4U you might want to use the following cheats in citra for QoL:
[Increase camera rotation speed]
00BFD2EC 41A00000
00BFD2EC 41A00000
00000000 41A00000
[FOV 60]
00C06D98 42700000
00BFF614 42700000
00BFF618 42700000
6105729C 00000000
B105729C 00000000
00000ED0 42700000
[Disable 3D]
610572CC 00000000
B10572CC 00000000
00006BA8 011F036E
D2000000 00000000
This is done by launching the game in Citra and then clicking Emulation -> Configure Current Game -> Cheats
If playing MHGU on Ryujinx LDN you may want to use the 120fps-v1.4.0 patch by theboy181
If you need/want further clarifications about anything let me know and I'll be glad to help. Also if you do decide to play one ask questions early and often (I'd also be down to play if you're ever interested). The older games start much slower. They usually give you some busy work quests (collect 10 special mushrooms, kill 10 small monster) before you really start getting into the core gameplay loop that you're used to in Rise. It usually takes about 1.5-2hrs to get to that point.
Also note these games are harder initially due to just different mechanics that you'll get used to. You have limited health potions; no restocking at a base camp- what you bring and what is in the supply box is what you get. Once you unlock the kitchen you have to eat before going on a quest as there's no in-quest kitchen available. To mine/catch bugs you need pickaxes and bug nets in your inventory (which can break). I've had pretty good success in getting new world players (World and Rise) into older games, so if you have further questions really do please ask.
Monster Hunter 4 Ultimate (3DS-Citra) or Monster Hunter Generations Ultimate (Switch - Ryujinx LDN build so you can play multiplayer). Generations Ultimate is a switch port of a formerly Japan-only 3DS game (MHGU is the English release) so if you're worried about emulated Switch performance it's one of the easiest to run games on that console.
MH4U is probably the best way to play the fully realized vision of the oldschool formula (mechanically it's "complete" in this game) and MHGU allows you to to either play with MH4U mechanics (Guild style in game) or with various twists (Valor, Adept, Alchemy styles) which radically alter the combat style of each weapon. I played through the game first in Guild style (because I didn't speak Japanese and only had that version at first until the international release) and while the game is completely beatable never using any weapon styles/hunter arts, the post-game content (Deviant monsters) are absolutely designed for you to use those things.
If you had to make me just make a gut call on what to try- I'd say MH4U.
If playing MH4U you might want to use the following cheats in citra for QoL:
[Increase camera rotation speed]
00BFD2EC 41A00000
00BFD2EC 41A00000
00000000 41A00000
[FOV 60]
00C06D98 42700000
00BFF614 42700000
00BFF618 42700000
6105729C 00000000
B105729C 00000000
00000ED0 42700000
[Disable 3D]
610572CC 00000000
B10572CC 00000000
00006BA8 011F036E
D2000000 00000000
This is done by launching the game in Citra and then clicking Emulation -> Configure Current Game -> Cheats
If playing MHGU on Ryujinx LDN you may want to use the 120fps-v1.4.0 patch by theboy181
If you need/want further clarifications about anything let me know and I'll be glad to help. Also if you do decide to play one ask questions early and often (I'd also be down to play if you're ever interested). The older games start much slower. They usually give you some busy work quests (collect 10 special mushrooms, kill 10 small monster) before you really start getting into the core gameplay loop that you're used to in Rise. It usually takes about 1.5-2hrs to get to that point.
Also note these games are harder initially due to just different mechanics that you'll get used to. You have limited health potions; no restocking at a base camp- what you bring and what is in the supply box is what you get. Once you unlock the kitchen you have to eat before going on a quest as there's no in-quest kitchen available. To mine/catch bugs you need pickaxes and bug nets in your inventory (which can break). I've had pretty good success in getting new world players (World and Rise) into older games, so if you have further questions really do please ask.