There are many difference choices when it comes to choosing insulation for your home. Choosing the right option will depend as much on your location and situation as it will on your budget, your need for soundproofing, the temperature where you live and whether or not you're building anew or renovating.
If you're considering insulation for a home you intend to build, then your options are wide open and you can accommodate any type of insulation you want. Adding insulation to an already built home can be trickier, since many of the cavities that will normally house your insulation have already been sealed off. Getting the insulation into the right spots without ripping out all of your walls can be achieved by drilling holes in walls, and then blowing insulation into the wall cavity.
The construction materials you use will determine how much thermal mass you're dealing with. Thermal mass is important, especially with very dense building materials like concrete and brick. These materials can store heat, releasing it long after the surrounding temperature has dropped. Other aspects of your home, like whether you're using double glazing in your windows, can also contribute to how you're able to regulate the temperature inside your house, and how much heat is allowed in.
The type of climate you're in will determine whether you want insulation that's designed to keep heat in, to keep it out, or to strike a balance between the two.
As an example, in hot climates, correctly installed reflective insulation is favoured over bulk insulation like glass wool or mineral wool as it prevents radiative heat from the roof entering living spaces during the day. Bulk insulation is increasingly important in northern climates though, mainly because far more people are now using air conditioning, which create much bigger temperature differentials between the outside and the inside of houses.
If you live near a major highway, railroad or any area with a lot of latent background noise, you might want to think about including soundproofing in your plans. Other areas of your home that you may want to seclude such as home theatres are also good candidates for sound insulation. How much of it and what type you'll need will depend on the level and frequency of the noise you want to isolate. Most thermal insulation already provides a certain amount of soundproofing, but if it's a particular concern then you'll need to choose carefully.