Well, it really depends. Get the aperture that your money will allow. A reflector is great for 75% of the people interested in buying their first telescope.
The reasons to buy a refractor are more complicated. Inexpensive refractors are well-known or having problems with false color, but they are easy to carry around while traveling. Please keep in mind that refractors have the tendency to give more pleasing view when used during daytime hours. Most reflectors are pretty big in size, but they have superior light gathering ability.
In short the answer to this will usually be no. In general terms you get what you pay for so if you want a really good telescope, you will have to pay for it. Once you have purchased a high quality telescope though, it may never need to be replaced. It can be viewed as an investment rather than an extravagant purchase.
A computerised telescope makes it easier to find objects that are deep in the sky. These are objects that might have otherwise have been missed, especially if you are new to astronomy and are still learning about the positions of the stars and the planets. The price of a computerised telescope has also come down quite a bit in recent years so they are generally more affordable but they will be more expensive than a regular telescope. However, there are some people that do not like using a computerised telescope because they do not believe that they will ever really be able to learn the sky without hunting for things themselves. Whether you choose to buy a computerised telescope or not will largely depend on your personal preference and whether you want to hunt for things before you view them or you are happy to have them pointed out.
The larger the aperture the higher the light and the resolution will be. A comparison between a 5 inch and 10 inch telescope will show that the 10 inch telescope will have four times the amount of light and twice the resolution. This can make everything that you see through the telescope much clearer, although you will have to bear in mind that if the sky is cloudy you will not be able to see that clearly regardless of the aperture.
There is no easy answer to this question as the telescope that you choose will depend on what you want to use it for. You will need to find something that you want to use and that you do not find too frustrating. This may mean that you end up not wanting to use the telescope at all which will be a big waste of money. One other thing that you will need to bear in mind is that there is a good chance that finding the right telescope is going to cost you a lot more money than you may have anticipated.
If you can not say for certain what you want from a telescope then you may be better off getting a pair of binoculars. This is not said to be flippant, telescopes are expensive pieces of equipment and it is a lot of money to spend on something that you are not even sure you will use that often. There are many good models of binoculars that are on the market that will be more than adequate for looking at the stars every now and again. The other advantages of binoculars is that they will not take up a lot of storage space when they are not in use. They can also be picked up and used as soon as they are needed without having to worry about setting them up.
If you just want something to impress the neighbours then this is another reason to question whether you really do need a telescope. They may well be impressed by seeing a telescope in your window but from a distance they are probably not going to be able to tell anything about the capabilities of the telescope. Therefore you may just as well go and pick up the cheapest telescope that you can find, but you should not expect to be able to see much through it if you do use it to try and observe the stars. If you just want a telescope to look at, a miniature model that will sit on your desk or shelves may be all that you need.
If you enjoy stargazing every so often but it is not a serious hobby, then as mentioned before, a good pair of binoculars will probably do everything that you need and this will also be a much cheaper option. If you do really want to get a telescope then a Dobsonian will probably be the best choice. This provides the best aperture for a budget telescope and is also very easy to use and set up.