Horse manure is really good for heavy soils and you'll be shocked by how quickly it vanishes from sight as the worms get busy.

Empty beds... Unless you've been in your new garden for a full year - don't count on them being empty. Sometimes things will 'pop up' even years later and spring bulbs are definitely among the 'poppers'.

Personally, I wouldn't lasagne over the top of such persistent woody weeds as ivy and canada thistle. See what you can remove by pulling, first, though those thistles are going to be seriously challenging and will probably need chemical intervention (spray). Don't bother composting any of them. Burn them if you can, or send them to the dump once they've withered beyond recovery.

A thick layer of mulch (up to four inches deep) - semi-rotted manure/straw mix mixed with grass clippings - on the bed where you've planted your shrubs will both keep down your weed population and feed the soil/plants. Keep it back from the stems, though, as it can encourage fungus. The birds will skritch it over and keep it stirred up for you. Apply in early summer, and mid autumn, while the ground is still warm. For the roses, add some potash fertiliser so they harden off to face the winter.

Also - check where those weeds have come from. If you have pasture lands nearby, or old gardens with those plants well-established, then you can expect to find seedlings year after year. (I have barberry hedges nearby and the birds are forever bringing in fresh seed.) Just something to be aware of.

If there are too many beds to manage for now - take out the troublesome weeds, roughly level the beds, then keep the weeds down with a weed wacker. You can always expand later, once you've regained control. :-))

For lasagne - start on a fresh site, if you can. Straight over the grass with your paper and cardboard.

Welcome to gardening and these forums!

Instead of constantly fighting with the weeds in the "really overgrown beds," it would be best to get started smothering them with lots of thick layers of cardboard, or even plastic, and something to hold it down when the wind blows, like rocks. You don't really want to weed-wack poison ivy at all anyway. I wouldn't recommend any further amendments until you know the already-growing ivy and thistles are gone for good. Chemicals do not usually kill thistles or english ivy unless you use really nasty stuff and/or apply it multiple times, so I wouldn't bother.

You'll need to be vigilant about sprouts of new weeds for a few years in all of the beds because it sounds like many weed seeds have been produced and allowed to fall right in the yard. Once those have all sprouted, you'll only have a normal amount of weed seeds brought in by birds and wind.

The distinction of "lasagna" vs. "amending soil" is a barrier of usually newspaper or cardboard that is placed at the bottom to smother existing weeds - but not weeds as tough as ivies and thistles. It's not usually practical or necessary around existing plantings. All you need to do in the area with roses & butterfly bushes is amend the soil by adding some compost and mulch once or twice a year. Weeds will still show up but will be easy to pull.

Weeding is much easier if it is part of what you do while admiring your flowers. When you let it go to the point where you realize "I need to go pull weeds," it's really un-fun and time-consuming.

You can also pile some leaves in the area (as long as they aren't mostly oak leaves) to encourage worms to take-up residence. Mother nature, with the help of worms and microbes, will redistribute nutrients from decomposing organic material at the surface into the soil where it can be used by the roots. Good soil structure takes years to develop and should not be disturbed except when you need to dig a hole for a new plant. The next time you dig a planting hole, use a dandelion fork or screwdriver to poke little holes at the bottom of the big hole. By just adding 4" of finely shredded hardwood mulch to heavy clay soil, it will be noticeably improved by next spring, and it will get darker, richer, with more improved tilth and humus every year as long as you keep adding compost and mulch to maintain the top layer.

Poison ivy (or oak or sumac) is a specialty weed in that the oil (urishiol) that gives people a rash does not die when the plant is killed. All parts: dead leaves, stems, and roots remain poisonous until it is decomposed. Urishiol can also retain its' potency for a long time on objects that have touched poison ivy. You should NEVER BURN POISON IVY (or oak or sumac) because the urishiol can become airborne and inhaled. It should be sealed in a plastic bag and sent to the landfill, not put with other yard waste where it might get included in municipal mulch. If you have a lot of...