1. don't get starter guitar packs, they suck.
I agree with this. I started with one of those fender starter packs about 6 years ago, the amps are bad, the guitars are cheap, avoid them at all costs
2. IMHO teaching yourself is better than being taught by a teacher due to you being able to learn anytime and go at your own pace, i also recommend getting a good handbook on guitars, i have one by Ralph Denyer its lasted me 5 years since i started playing.
I think this is different for every person. For me, I really liked being able to ask someone questions as I was learning. Granted guitar was my first instrument, and you already know piano so you may not need a teacher, but I still would say having a person is a lot better than having a book.
3. as for amps, you should look for combo amps that have built in effects, instead of buying all the pedals. Roland Cube combos are very good for starters, i got one and its very good and has lasted, if you get the cube aim for the 20XL and above. Line 6 do good small combos so check them out.
Combo amps can be nice, but you don't exactly get the same feel of a pedal. About 4 years ago I bought a line 6 combo amp, but since then I've bought a couple pedals, simply because you have a wider range of effects and they tend to have a better sound to them. I plan on upgrading to a nice no frills tube amp this summer, simple for the sound. Although if your looking for cheap combo amps are good.
4. now for buying a guitar, if you want an SG or a Les Paul then go for the epiphones because its a Gibson without a few Gibson touches like the tuning pegs and headstock, also the Pickups. Ibanez have good cheap guitars for sale look for the Japanese built GIO series Ibanez guitars because they are VERY good quality and are cheap! If you can go for something that's more than £250, then you can find good fender squier guitars and ESP guitars. now if you want to go from £400 up to £700 then you can get a classic Epiphone Les Paul Standard and high quality reissued Fenders, all the way to i Gibson SG.
Do not buy an epiphone. Personally I'm not a big fan of Gibson, they charge more than their guitar's are worth IMO, and the epiphones are even worse. You are buying a look, not a sound. I play a paul reed smith, IMO they sound amazing. The model I play is this

an SE singlecut. The SE stands for student edition, which is a bit cheaper and you don't get all the bells and whistles, but I think the SE's sound better than any other guitar on the market in that price range. Mine cost $500 dollars, and I think it sounds better and feels better than my friends $800 epiphone SG. However I do agree that Ibanez makes good guitars. They make a solid guitar for the price range, and you can not go wrong with them
That's just my two cents, hope that helps.