I would consider updating the electrical system. Its an easy way to provide added value to your home and not to mention the added safety for you and your family.
Also remember that dirty connections cause increases loads and create heat. If one appliance seems to dim the lights more than others, the receptacle may have dirty connections. Also look for dirty connections where the fuses screw into the box. Look for dirt and feel for heat.
If you cannot afford to update the entire electrical system, do what makes sense. If the box is real bad, think about updating it first. You can at-least replace old receptacles and/or wiring where you are drawing the greatest loads.
One last thought, if you have lamps dimmed with a dimmer, you will notice the effect of starting appliances much more than on lamps that are not dimmed. This is normal.