I’ve not had a single problem with my HP bought last year. i7 processor and 16GB. I’m in process of setting up an M-Audio USB mixer to plug into it.
Most laptops are pretty good these days. I've been having good luck with Acer recently, so If it were me I'd probably buy this:
8Gb Ram and an i7 processor should be adequate for most live looping. You could swap out the drive for a SSD (solid state drive) if you have a large number of tracks of music being written to or read from the disk.
The biggest question mark is your sound card. Most people anymore use a USB sound card, and not all chipsets work equally well with USB audio. I would post in whatever forums there are for your particular sound card and find out what laptops have worked for other people. I'm currently using a pretty inexpensive Focusrite Scarlett 2i2 USB sound card and I'm getting low levels of latency that rival expensive RME sound cards.
With a $1000 budget you should be fine. Stick with lots of RAM and a top of the line Intel i7 processor and you will probably never come close to the limits of the machine.