I think I would start right next to the house and take back any branches that are scraping on the house walls or roof or gutters.

I would also check the gutters to see that they are free of old rotting leaves and that the downspouts and drains for stormwater are clear. If you get sudden rain events then this can be very important. If you have metal gutters rather than plastic - check that leaves have not caused rust and little holes. (Somehow there is always a leak in the gutter over the back door...;-) )

Then I would look at the trees in the yard that give really good shelter in the summer. They make cool patches for kids to play in and for you to put out a table and chairs in the shade. You might need to take out surplus shrubs and plants to give yourself the clear room to use.

You would want to be able to get there easily, so have good wide paths from the house to these places. If they are hard-surfaced then a child can ride on toys or pull waggons along them.

Some of the trees and shrubs might have branches and leaves low to the ground and would look really awful if those branches were taken off. (Some evergreens grow that way.) They can act as a living wall in the garden - screening off private areas. If you were to take them out, for good safety reasons, you might need to consider how else you will get that privacy.

Older shrubs with dead branches and such: some plants don't live for very long. For example, you might find that California lilac (Ceanothus) only looks elegant for about fifteen years and then it becomes quite woody and gnarly. It has character - but a lot fewer flowers than a younger plant. Gnarly? Or flowers? If it's flowers you want then you'll take out the old plant and replace it (or enjoy the space).

If branches are dead you can take them out at any time of the year. Be particularly careful when you have to work higher than your head. It might be slower to remove a limb in small sections but it doesn't hurt nearly as much if a piece falls on you!

For the vines: sometimes they are planted to give a big sheet of flowers and scent, or to cover an old tree or fence and to hide a bad view. And some of them are planted to give 'instant' results. Many 'instant' plants have thug tendencies. They grow vigorously...

Before you take to the stranglers - take a look at what will be left once they've gone. You might be willing to leave some of the vines behind because of the effects they give - or the shelter.

If the honeysuckle has really got away and is out to monster the garden you will probably need loppers that will cut through at least an inch, a pair of good secateurs with brightly coloured handles so you can find them in the tangle, possibly a pruning saw. (Don't waste your time trying to cut vines and dead branches with a carpenter's saw. The teeth are too small and not set right to shift away the green wood as you cut. A swedish bow saw might be fine but a pruning saw will save you a lot of hard work.)

And you will have to dig out the roots (or use a strong herbicide stronger than Roundup), so a mattock or sharp spade will be useful.

If you don't recognise all the vines, and you have a digital camera, take photos, then post them on the Name That Plant! forum (there are instructions available) to get answers and leads on how to live with them or control them.