I don't think it matters whether you give apples or bananas, or carrots first. I have always given mine banana first simply because it is so easy to prepare - choose a nice ripe one (probably riper than you'd like to eat yourself), put about a third of it in a bowl and mash it thoroughly until it is virtually runny. It is rather slimy, which helps it slide down easily! But beware, any clothes it gets on get stained black, so use a really ample bib (or have your baby naked if its warm enough!)
As for apples, choose any sweetish ones - pink lady are very sweet, and I just cooked up some braeburn which didn't strike me as sweet, but the resulting mush was very sweet. Just don't use cooking apples!
I peel and core the apples and then steam them, but they can be boiled, too. To begin with they need to be cooked lots, until they are very soft, but after a couple of months they can be cooked less (cooking destroys some of the goodness). I mash them with a hand held blender, but they could also be passed through a sieve. I use the steamer and the blender for most veg - carrots, cauliflower, broccoli etc.
Some things can be baked, which preserves more goodness - butternut squash, sweet potato, regular potato. After baking for an hour or so, they get mashed with the blender, or get put through a mouli (my new baby food toy!).
As for freezing, they last a few months in the freezer (depending on the freezer) by which time your baby will be eating different foods and consistancies. I always freeze it in ice cube trays.
I find it rewarding and easy making all my babies' foods. My older two (4.5 and 2.5) are big eaters who like most foods, and it is probably luck, but I like to think it is partly to do with having eaten lots of different foods from a young age. When you prepare food at home the consistancy varies from batch to batch, so they get used to that, too, which helps when starting on more lumpy food later.
Hope this helps!