1) It's sort of an AFK and slow grind thing. You just go to certain spots at given levels, harvest from wisps, and turn them. Occasionally you get chronicles redeemable for Hunter XP as well. It isn't really all that complicated - there are a couple of summoning familiars that can assist you if you have requirements, but that's about it. There is also a useful Distraction & Diversion called Guthixian Caches that can get you some experience each day for playing, and temporary buffs. I would recommend taking advantage of that to its full potential and pacing yourself accordingly if you really want to avoid the grind.
2) Ports is worth doing if you want higher level armor and want to go boss. I could be wrong, but I don't think it's absolutely necessary by any means if your sole ambition is to chase the quest cape. After all you can spend a few hours killing things and earn cash for a degrade-to-dust T90 set instead if you really needed it. But then again, might be worth doing. Herb runs can still make a decent profit. You can do broad arrowheads, vis wax, and wicked hood runs as additional dailies to make more. There are probably even more/are often improved if you have completed more tasks and achievement diaries around RS, so perhaps someone can fill in a little more for me.
3) Frost dragons should be nice and steady, assuming you have 85 Dungeoneering. You should be able to bring a war tortoise and minimal food, along with notepaper, and camp there quite a bit. Other than that, GWD or just Slayer can be a decent option, but that might be about it. KQ, chaos elemental, or barrows are certainly possible, but each have their own issues and are not really up to par in loot.
4) Acquire a set of drygores, bandos, armadyl, subjugation, rcb, and armadyl battlestaff or virtus wand/book would be what I would recommend to stay in that budget.
5) Abilities from The World Wakes are useful to go unlock, as well as ones from post-Dig Site. Talk to the archaeologist to get them - you meet all requirements. The dragon rider necklace is a decent item for all-around necklace slot, and is obtained off One of a Kind, another quest. The asylum surgeon's ring from completing certain challenges in yet another quest (Broken Home) is a useful ring that has a chance to use no adrenaline on a threshold ability and has good strength bonuses in all three classes.
Legacy mode functions okay for most routine combat, but EoC pretty much outclasses it for almost everything except abyss training for barrage/chinning. I do not have much experience with Legacy mode so I am unsure how much of a handicap it is, but I would advise you to give EoC a try.