The range of work you can do is covered on the HSE site about asbestos, and it's actually quite extensive.
It largely depends on the friability of the material in question. Things like spray on insulation and loose fill insulation which can shed fibres easily... licensed work, steer well clear. Things like artex, cement/asbestos guttering, downpipes, roofing sheets, floor tiles... generally things where the asbestos is retained in substrate... non-licensed materials and with appropriate training you can deal with yourself.
A good example for us is a cable penetration in asbestos insulating board. If you need to make a hole in AIB, it's non-licensed work that you can do with training providing you follow the guidance from the HSE. Their guidance takes the form of method statements for the tasks you can carry out and they provide a decision support flowchart to aid you in making the right decision.
Another good example is changing a light bulb in a fitting mounted on AIB insulating board. The fitting is considered to be contaminated and so has to be dealt with properly using the HSE guidance.
You should be aware though that some work items are notifiable to the appropriate agency (either the HSE, the local council or some organisation to do with the railways). If you do these types of job, you have to have a medical at the start and then every 3 years, keep those records for 40 years I think and obviously notify the work (the HSE may rock up to check things over).
As for the overalls... the only things I didn't dispose of in the asbestos waste bag from my hole boring were my respirator (which I bought specifically for this), my tools and the containers I use to store the wallpaper paste (which keeps the dust under control) and PVA (for sealing the edges). Everything else went in the bag for disposal.
Currently I have four bags of asbestos waste from the property. 1 contains a collapsed piece of plasterboard with artex on it, 1 contains artex that was coming off the ceiling due to a water leak and more pieces of plasterboard with artex on I found in the loft, the dust from cleaning those bits up (you spray with a fine mist of water to keep the dust down), the dust pan and brush used to sweep up the damp bits and the wet wipes I used to finish off cleaning up those bits and the other two contain overalls, boot covers, wipes, bits of plaster board and dust from the hole boring activities and the polythene sheeting I used to protect the floor.
In essence, you throw away nearly everything that cannot be wiped down easily.
Disposing of the waste... find a local specialist and have them pick it up or get yourself a waste carriers licence and transport it yourself to a licensed disposal facility.
And as
@Rosco stated you have to have a suitable respirator and you have to have a face fit test to prove it doesn't leak.
If you use a class H vacuum cleaner, you can't open it. It has to go to a specialist to be emptied and as such needs to be transported carefully. I'm dealing with a company called SMH Products for supplies for this kind of work. They are specialist providers where you can get all the gear and hire equipment. The peeps at the Cardiff branch have been really helpful.
