First you have to go through Mt.Moon and then go on to Cerulean City and beat Misty. After that you have a little run in with Gary and then get a S.S. Anne ticket from Bill after helping him. Then you have a little run in with Team Rocket and after that, you make your way to Vermillion City where you have to go through S.S. Anne, beat Gary again, and get HM 01 Cut. After that you defeat Lt. Surge. Go through Diglett cave and then use cut on the tree beneath the house. Go through into the building and one of Professor Oak's aides, will give you HM 05 Flash if you have caught at least 10 Pokemon.
Head back to Cerulean City, and there is a path that branches off from Cerualean where you will see a tree. Cut it then defeat all of the trainers. Make your way down this path and eventually you will reach a dark cave. Go through this and defeat all the trainers then when you reach the end of the cave, you will be in Lavender Town.
In order to catch Lavender Town Pokemon (I assume you mean Haunter/Ghastly/Cubone etc.) you have to head West to Celedon City and defeat Giovanni at the Team Rocket secret hideout at the Game Corner for the Silph Scope which will allow you to progress up Lavender Tower and catch Ghastly and Haunters.