If it were me, I'd till and plant rye this fall (real/cereal rye, not ryegrass). Then drill alfalfa straight into the rye come spring. The rye will look a little macerated after you pull the drill through, but as long as it's not too far along it'll come back quickly. Let the rye grow for a month or so and cut for green feed. As long as it's nearing the point of heading out or later, cutting it will kill it. That's pretty common practice in many places to get an early forage crop off a new hay seeding. My best alfalfa field is actually one I did similar to that: It was in a very (veeery) sandy field that was corn stubble when I got it. I wanted to put a cover in just to hold the soil together over winter and add a little organic matter. I broadcast rye in October, ran a light set of discs over it to get a little incorporation, and I wasn't expecting much. The rye surprised me and came up unbelievably well. I then took a gamble in the spring and frost-seeded alfalfa into the rye at about 25#/acre. It all came up together, then the rye took off and the alfalfa looked pretty sparse/stunted. But after cutting the rye, the alfalfa exploded, and there are pretty much no weeds thanks to the suppressant power of the rye.

Sprays are, of course, another option. But I try to avoid sprays wherever possible. I'm not a tree-hugging hippy by any stretch (quite the opposite), but once you've ben to a few soil biology seminars and work with a few large-scale organic folks, you realize just how harmful any spray is on the soil's microbe activity, which more and more people are quickly realizing is critical for soil health and disease resistance. As a comparison: I have two alfalfa fields at my fathers; one was planted in a field that was in a round-up-ready corn/beans rotation for years, the other that was fallow ground for a couple of years prior to breaking it up. The alfalfa looks great and almost identical in both fields, but if you pull shoots and look at the roots under a glass, you'll see almost no nodulation in the field that was round-up'd, versus crazy nodulation in the field that was fallow. It's quite something to see/compare, and has really convinced me to pay more attention to my soil's biology. The fallow field also comes back a lot faster between cuttings and looks a lot greener in the late fall.

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Drill winter rye grain six to eight weeks before frost to have a maximum stand in spring.

I'm mixing buckwheat this fall with the rye. Maybe clover. Those three hand out NPK.

If you disk the rye down in spring you waste it. 

Plant corn beans into standing rye either strip till or using row cleaners (corn beans need hotter ground to germinate than covered in rye mulch). Then once the corn beans are up, you terminate the rye (rolling or chems). That blocks most weeds. Roller-crimper is best for single pass but I've had good success with a flat cylinder roller or cultipacker going down and back since any stand up comedians get flattened the second way.

Weeds tell you the soil is compacted or missing something. Fix that issue and the weeds vanish. Otherwise there is a thousand year seed bank to fight.

If you can manage it, between four and eight plant cover crop species mix give synergistic results. Weeds can be part of the mix ;) or so they say.

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