This is my first walkthrough and I really don't have anything to refer to if I'm doing this right, so I appologize if I'm doing this wrong.
Gym leaders
Roxanne- rock types, 2 Geodudes lvl 12, Nosepass lvl 15
Brawly- fighting types, Machop lvl 16, Meditite lvl 16, Makuhita lvl 19
Wattson- electric types, electrike lvl 20, voltorb lvl 20, magneton lvl 22, manetric lvl 24
Flannery- fire types, slugma lvl 24, numel lvl 24, camerupt lvl 26, torkoal lvl 29
Norman- normal types, vigorath lvl 27, spinda lvl 27, linoone lvl 29, slaking lvl 31
Winona- flying types, swablu lvl 29, tropius lvl 29, Pelipper lvl 30, Skarmory lvl 31, Altaria lvl 33
Liza+Tate- psychic types, xatu lvl 41, Claydol lvl 41, Lunatone lvl 42, Solrock lvl 42
Juan- water types, Luvdisc lvl 41, Whiscash lvl 41, Sealeo lvl 43, Crawdaunt lvl 43, Kindra lvl 46
E4
Sidney- dark, lvl 46-49 Mightyena, Cacturne, Crawdaunt, Shiftry, Absol
Pheobe- ghost, lvl 49-51 Dusclops x2, Banette x2, Sableye
Glacia- ice, lvl 50-53 Sealeo x2, Glalie x2, Walrein
Drake- dragon, lvl 53-55 shelgon, Altaria, Flygon, Kingdra, Salamance
Wallace- water, lvl 55-58 Tentacruel, Wailord, Ludicolo, Whiscash, Gyrados, Milotic
Steven(after beating champion. In Meteor falls, waterfall required) lvl 75-77 Skarmory, Claydol, Cradily, Armaldo, Aggron, Metagross lvl 58 (Idk why either....)

Each gym leader is a decent challenge if playing on a real game boy, so its best to take advantage of vizzed's Fast-Forward privilege. Go in patches of grass that have the toughest wild pokemon available before facing a gym. I always make sure all my pokemon are at least 5 levels higher than the leader's toughest, so I won't worry about using potions. This also prepares you for whatever trainers await on the trip to the next town.

When trying to catch a pokemon, press f2. Get as close as you can to killing it, without actually doing so, then press f2 again. Now, hold the spacebar and see if you caught it. If not, then press f4 and try again. Each pokemon and pokeball has a different capture rate, so that means that there is a chance you can catch a pokemon, and a chance you don't. If repeated the process 30 times-just an exaggeration-you will be sure to catch the pokemon at least once. You will also need to experiment with different pokeballs. I always think ultra balls takae the majesticity out of legendary pokemon if caught, so I use pokeballs or great balls. That is just my personal opinion though...

There is a similar pattern when trying to land a critical hit. Some items or moves state, "raise crit hit ratio, RATIO". There is a chance to get critical hits too. If you are facing a trainer with advanced healing potions like the E4 or champion, land a regular hit that does atleast 1/3 of their health, and then aim for a critical hit. So hold space and press f2, hit, and if didn't work, f4 and try again. Doing the f2, f4 method does take minutes until achieved, so sometimes it is just not worth it... Let me point out that this technique also works for less accurate moves like fissure or blizzard, or even just using thunderbolt and trying to paralyze a foe. There is a chance that you can get what you want, you just need to hope lady luck is on your side.

When searching for a rare wild pokemon, hold space, f2, run around. If you didn't find the pokemon, press f4 and try again. Again, rare pokemon have a chance to appear too, just less of a chance than common pokemon like magikarp. This is from experience; Don't run in the same spot if you press f2 and f4, because the same pokemon will appear. That means if you can only take 2 steps and you always run in the same direction, you will see that same pokemon appear until you run in a different direction. I found this out myself while playing pokemon Shiny Gold X and the same rule applied here. You must always run in different areas to get different pokemon.

Useful Rares: Ralts, Seedot- rt 102/ Slakoth, Tailow-Petalburg Woods/ Skitty- rt 116/ Grimer-Fiery Path/ Seviper-rt 114/Bagon-Meteor Falls (in spot you meet champion steven after beaten Wallace. Move waterfall needed. Find youtube video if need help)/ Elecrode, Magneton-New Mauville(very rare)/ feebas-rt 119 surfing (very rare)/ tropius-rt 119/ Absol-rt 120/ Chimecho, Duskull- Mt pyre Summit(in grass where archie appears)/ Relicanth-Underwater grass
These pokemon are all not commonly seen in the game, so if you are interested in finding any, please do.

In every pokemon game, I balance my team out with many types. Usually my teams have at least 9 different types, so I have a wider variety of moves. I have Blaziken, Crobat, Ludicolo, Gardevoir, Manetric, Linoone. Try and make sure that a pokemon doesn't have types weak to the same type. I.E. Dragonite is 4x weak to ice attacks, Golem 4x weak to water, grass moves, Swampert weak to 4x grass moves. If you happened to get a critical hit, then it'd be 8x the damage, more than enough to kill a pokemon.

A helpful feature in emerald is the Match Call. This is similar to Gold and Leafgreen's Vs. Seeker. Match Call allows you to register trainers (if they want) and rebattle them again if they are ready. A little icon in the shape of a pokeball will appear next to their name if they are ready. Tip: Go in rt 117(between mauville and verdanturf). Stand in front of the twins, and walk down to the trees until you can't walk anymore. run straight to the left and straight to the right. If done correctly, you can run from Verdanturf to the right of Mauville. Repeat this process over and over again, while holding the spacebar. After a while, talk to the breeders, twins and triathletes (if already beaten) and they will want a rematch. The breeders have lvl 31 pokemon x6, athletes have lvl 37 dodrio, and the twins have lvl 38 x2. This helps exp farming if you are not at the elite four yet since each pokemon gives about 1k exp.

Another way to battle trainers are a reporter and her cameraman. They appear in 3 places: rt 111 right after those two rocks before the desert, 118 after surfing across, and rt 120 (the right side of fortree city). They have lvl 39 exploud and magneton. you can battle these two as often as you want as long as you know the order they appear in (111,118,120, repeat) they give almost 4k money which is also good. It helps a lot to a pokemon that knows earthquake, surf, water spount, eruption, does damage to both pokemon.

There are a few legendaries in this game. Rayquaza, Groudon, Kyrogre, Latios/as, Regi x3. This is long enough already, but you can on youtube and find out how to get them all. Hope this helps