For $1000 you might want to see if there are some good used pieces available on AudiogoN. The turntable you might want to go for new, so the ProJect Debut III in black for $350 delivered would be a sound basis for an entry level vinyl system.

Loudspeakers are often subject to personal preference according to how they sound and you might want to try to audition some in the $500/pair or less range. A pair of used Magnepan MMGs for $350-$400 are always a good bet as far as I'm concerned. There are a whole lot of closeouts right now on decent bookshelf speakers like the PSB Image B25 for $320.

For distribution and power, again buying used could help maximize your investment. You'll need a solid stereo receiver or integrated amp with a phono section. If you find a good deal on something without a phono section then you will also need a budget phono preamp. I see a like new NAD C326BEE or Cambridge Audio 640A on AudiogoN for around $300. Good budget phone preamps you might find used are the NAD PP2, Parasound Zphono, Cambridge Audio 540P. The AudioTechnica PEQ3 is an overachiever and can be had for $44.

Your listed chain of components is correct. If you are putting together a two channel music system for listening to vinyl you would not want a home theater AV receiver. There is way too much AV functionality and features you would not take advantage of in a music only system. A used in good condition NAD, Cambridge Audio, Music Hall, Denon, Marantz, Onkyo, Rotel, etc., stereo receiver or integrated amplifier would be in order.

Check on wwww.accessories4less.com and look on the left hand col for home audio and then find receivers. There are usually some Marantz stereo receivers with built in phono stages and possibly some Onkyo units at good prices.
Accessories4Less

If you want the FM radio that receiver would be servicable. It also has a phono input. Although the Epos ELS-3s sound good, I'd think about spending more and getting the PSB Image B25s in closeout for $320/pair delivered from DMC Electronics. They are a better loudspeaker having better bass extension and are more efficient. http://www.stereophile.com/standloudspeakers/1204psb/index1.html

That Marantz PM5003 is an integrated amplifier which does not have an FM radio section like a stereo receiver would have. If this is primarily for vinyl it would work well as I believe its sound quality would be a bit better than the Onkyo previously considered. Good Luck!