AIS says 1.2-2.0g protein per kg bodyweight daily.
For you as a 60kg bloke, this is not a heap - 72-120g. Meat is about 25% by weight protein, nuts 10-20%, rolled oats 17%, most starchy food like rice etc has 5-10%, etc. So you have porridge and milk for breakfast, then get a big chicken breast (they're 250-300g) and have it for lunch or dinner (or split between them) and a handfull of nuts, that takes you to around 100g protein. The vegies and fruit and so on you have will easily knock you over the 120g max beyond which not much more protein will get absorbed. No worries.
Protein is not all you need, though - you need fats, carbs, and vitamins and minerals. So you need good food, and lots of it.
The key thing for
you will be a
caloric surplus - taking in more than you spend. To be 6ft and 60kg suggests you don't have a big appetite, and/or are quite physically active already. So you are really going to have to eat a
lot.
Lots of fresh fruit and vegies, nuts and beans, some meat, fish and dairy - and lots of starchy foods (rice, pasta, bread, spuds). I mean LOTS. If you
ever feel hungry then you're not eating enough.
You see, your body wants to stay as it is. Hunger means it's short of food, being satisfied means it's got just enough - to stay as it is. You don't want to stay as you are, you want to get bigger. So you have eat even when you're not hungry.
You don't need
protein powder at all, you just need good food. What protein powder is good for is two things.
Firstly, it's good to have carb and protein immediately before and immediately after your workout - it gives you fuel for the workout, and helps you recover and grow afterwards. If you had steak and spuds or something you might lose them during the workout as you chuck them up. But a drink is digested pretty quickly. So the protein powder can be good for that.
Secondly, it's good for when you find it difficult to prepare food, or physically difficult to eat another meal. 500ml milk + 100g skim milk powder + 3 eggs is 70-80g of carbs, same of protein, and 45g or so of fat - 1,000 kcal. That would be like a big steak with vegies and a some garlic cream sauce. The drink can be prepared in under a minute, and sculled back quick; the steak and vegies and sauce would take a while to prepare and eat.
Some people who find it hard to eat so much just get the extra calories and protein from milk - work up to 4lt/day (not a typo). 1lt/day in the first week, 2lt/day in the second, and so on. But still you need good nutrients in the rest of your diet, you can't live on milk!
For a beginner wanting to gain a lot of weight, I don't think you need protein powder at all - it doesn't do any harm, but it's not physically necessary. Just eat well, along the lines I noted above. For your workout take along a litre of milk and drink that instead of pure water.
The cheapest protein/carb weight gaining powder is milk powder. $6 for 1kg (you can get it cheaper in bulk), each 100g has 35g protein, 55g carbs and 10g fat, about 450 calories, something like that. 100g powder is 1 metric cup.