When I said "That's why one of the previous posters recommended dealing with the Pokedex completion in the sixth generation games," I was referring to your need to trade in order to complete your Pokedex, whether to obtain version exclusive Pokemon or evolve those that only evolve by trading. While you could get all of the Pokemon by owning the games yourself, you'll need to be able to trade with yourself to do so. That requires multiple game systems in the older games, but with the current, wifi-enabled generation, you can trade with other people to obtain all of the Pokemon without needing more than one game system.
For the most part, GameFreak has tried to make all of the Pokemon (or almost all of them) available within the games of a particular generation. For example, the generation 6 games (ORAS and XY) allow you to obtain many of the starter and legendary Pokemon from other regions. For instance, you'll be able to choose one of the Kanto starters, Bulbasaur, Charmander, or Squirtle, shortly after you earn your first badge in XY. However, to obtain the other two, you'll either need to trade, transfer them from previous generations, or get their second-stage evolutions via Friend Safari. (Don't worry about friend safari right now, just be aware that it's a way of obtaining additional Pokemon that requires you to beat the Elite Four and add other users' 3DS friend codes.) So you can get these Pokemon within the sixth generation, but you can't get all of them on a single file without trading or interacting with other people. As a general rule, new generations do include previous generations' Pokemon; however, how to obtain these varies, and in some cases, you'll need to wait until after the main game (post-Elite Four) or play one particular game within a generation to obtain them. There may be exceptions (I know that was definitely the case for gen 1 legends and starters in gen 2, and it may have been the case in gen 5 with the legendary birds), but in general, you can find most current and old generation Pokemon within a particular generation.
As for equipment you'll need, it really depends on just how extensive you want to be in your Pokedex completion at each stage. Do you want to fully complete the Pokedex within each generation (in which case you'll need to play almost every game), or are you ok playing the main story for each game, transferring your team forward, and dealing with Pokedex completion in XY or ORAS?
For a minimalist playthrough (the games you mentioned, worrying about Pokedex completion at the end but transferring your team forward each time), you'll need:
--2 DS systems (if you're only playing FRLG and don't plan on trading, you won't need a GBA or GBA SP; just transfer at the end to HGSS. You'll need two of these to transfer from gen 4 to gen 5.)
--1 3DS (or 3DS XL, or 2DS) system
--One copy of each game of interest (if you're willing to wait until the end to complete your Pokedex, you don't need every game, just one from each pair)
--One annual subscription to Pokemon Bank, and the accompanying transfer tool ($5 for a year for Bank, buy it in the 3DS eShop; PokeTransfer is free)
With this approach:
1. Play FireRed or LeafGreen using the GBA slot of the DS. Note that you won't be able to trade at all, so you won't be able to complete the Pokedex along the way.
2. Play HeartGold or Soulsilver on the DS. At the end of the game, you can transfer Pokemon from FRLG to HGSS via Pal Park.
3. Play Diamond or Pearl on the DS. Trade everything from HGSS to DP using your 2 DS systems.
4. Play Platinum on the DS. Trade everything from DP to Platinum using your 2 DS systems.
5. Play Black or White on the DS. Transfer from Platinum to BW using your 2 DS systems (one with BW, one with Platinum).
6. Play Black2 or White2 on the DS. Trade everything from BW to BW2 at your earliest convenience.
7. Play XY on the 3DS. Download Pokemon Bank and PokeTransfer and move your Pokemon from BW2 to XY.
8. Play ORAS on the 3DS. To avoid buying a second 3DS, use Pokemon Bank to transfer your team from XY to ORAS. Use the GTS, Wonder Trade, the trade boards here, etc., to obtain the rest of the Pokemon you need and/or breed/train to complete your Pokedex.
That's probably the most doable route, though it doesn't really involve completing the Pokedex at all until gen 6. Still, many of these games aren't cheap these days, so if you plan to buy physical copies (and game systems to go with them), this is probably your best approach.
If you want to complete your Pokedex in each successive generation, you'll need to take a more comprehensive approach. Additionally, there will be some event-only Pokemon that you will not be able to obtain. That being said, if you want to do that, I believe this is what you will need for each step:
1. Completing the Kanto Dex in FRLG:
Equipment needed: 2 GBA systems, both game versions, 2 wireless adapters or a GBA link cable. (If you want to complete the 386 Pokemon national dex in this generation, minus events, you'll want to use the GBA link cable so you can trade with RSE.)
Just like with Red and Blue, using these two games, you'll be able to catch the first 150 Pokemon.
2. Completing the Hoenn Dex (optional, do this only if you want to complete the 386 national dex):
What you'll need: Ruby and Sapphire, GBA link cable, 2 GBAs.
3. Completing the 386 National Dex (minus events):
What you'll need: FRLG, RSE, Colosseum, and XD (the last two are GameCube games; I don't think you actually need all of these, but I would need to look up exactly which combination you need to complete your national dex; I want to say you can do it with RSE/LG/Colosseum, and maybe one of the other two games, but I'm not sure). Also, a GameCube, one or two GBAs (you can trade with the GameCube game with only one GBA, saving you a GBA, if you want), and a GameCube/GBA connector cable. The GBA link cable is optional in this case, but if you completed the Kanto Dex first, you'll already have it by this point.
3. Complete the Johto Dex.
What you'll need: 2 DS systems, both HG and SS.
4. Complete the original (non-expanded) Sinnoh Dex.
What you'll need: 2 DS systems, both Diamond and Pearl.
5. Complete the expanded Sinnoh Dex.
What you'll need: Platinum plus what you already have up to this point.
6. Complete the 493 National Dex (minus events).
What you'll need: 2 DS systems, DP/HGSS; don't recall if you need Platinum for anything or not.
7. Complete the Black and White Dex.
What you'll need: Black and White, 2 DS systems.
8. Complete the National Dex in gen 5.
What you'll need: BW plus the gen 4 games. BW2 are definitely worth playing and may make this easier, but I don't think you technically need them.
9. Complete the Kalos Dex.
What you'll need: 1 3DS, either X or Y, an internet connection that works with your 3DS (if you're using an enterprise network like those found at some universities, you may have problems, but if you have your own router/network, you should be fine). If you are someplace where you can't get your 3DS to connect, phone hotspots can work too.
10. Complete the ORAS Hoenn Dex.
What you'll need: One 3DS, either OR or AS, and an internet connection that works with your 3DS.
11. Complete the gen 6 national dex.
What you'll need: Technically, just one 3DS, one gen 6 game (OR or AS if you want all of the megas), and a working internet connection. If trading with yourself for trade evolutions, you'll need 2 3DS systems. Otherwise, you can use Bank to move your own Pokemon from one game to another.
That second list was probably long and somewhat confusing. You're probably best sticking with the minimalist approach, and getting an extra system or two if you want to play all of the games and trade with yourself.
Hope this helps somewhat. Let me know if you have more questions.