#1 and #2 you can use a long surf rod setup with medium salt water spinning reel. However that long surf rod won't work well for #2.
So Based on just these three your best bet would be to get a high quality medium size spinning reel like the Penn Battle Series. Dont get a big one, and dont get a small one. Somwhere in the middle will work. String it with 15 to 20 lb mono line. Then get (2) poles. Don't worry about he name brand on poles so you can afford 2. Honestly you can go pretty cheap on the poles and still be fine as long as you pick poles that are well made they will still last without the huge cost. Look for double supported eyes. For the bottom fishing you want a long pole (around 8 - 9 feet), medium action. Dont make the mistake of getting a long stiff pole... they cast like crap. You will get much further distance with a good flexible long pole. For the lure / plug casting you want a shorter, lighter, flexible pole. Light to medium action. Preferably about 6 feet. It will be a little bit heavier of a reel then I like for this kind of setup, but it will work.
PS, most surf rods come in 2 pieces. Shorter 6 foot rods that break into 2 or 3 pieces suck IMHO, and I would avoid them if possible.