I operate a few VPS servers on various networks such as Rackspace, Amazon, Cloud Shards and UK2 and what I find is it depends really depends on the cloud platform they use. Generally you have their own cloud software or they use some commonly known software such as OpenVZ, Xen and KVM.
You should start looking a the difference between each platforms and see what they offer, for example OpenVZ it is possible to oversell while XEN since it allots each user a SET amount and you can't set share resources you know that your server may be more responsive all the time while OpenVZ may have spikes at time but may offer more proformence at times too.
I have tried many times to get apache2, mysql and various other server related software running on 256mb and it always runs into problems. I would say the bare mininal you should be looking for is 384 to 512mb. It's worth noting that most NON-OpenVZ platforms do not allow use of the SWAP space since constant disk usage has a stain on the network, however on VPS's that allow SWAP you will easierly get away using 256mb or lower depending on the amount of swap they allow (Most companies you need to read the small print on this or contact them. Using swap on some actually breaks the terms and conditions - Rackspace for example).
Recommend Platforms I've First Hand Experience
Amazon is really good for affordable VPS solutions and since you only want to run WordPress you might get away running the Micro Instance which is 'FREE' for a whole year as well as using their RDS service which means you can host your SQL on an instance which means the Micro Instance has more free resources. Uses Ubuntu or Amazon Linux - Doesn't allow for Debian as far as a I know.
I strongly believe in you get what you pay for and if your not scouting for the cheapest option and want 24/7 support at a few clicks of a button and 1min wait queues without having to submit silly tickets that you just eagely wait for then Rackspace is the best and I've never had a company in web related services offer better customer service. Their cloud VPS is very fast and stable but of course they are not the cheapest bang for buck.
Weak Control Panel, But the VPS operates fast and you get a lot of resources for your money, there support is pretty crappy though and the support number can be expensive for long calls.
Only been with them for a couple of months and its run on a OPENVZ platform and I'm suprised how quick it is, the support they offer is ticket based but I normally get a good response within an hour.. By far the cheapest - I think I pay around $3.5 a month for the same that I pay rackspace at $40 a month but of course Rackspace offers more but as a cheap solution I recommend CloudShards.
Seriously, I believe that GoDaddy should stick to what they are good at 'SELLING DOMAINS' the shared hosting accounts I've had have a lot of downtime as well a the VPS services and even my shared hosting accounts have been hacked a few times while I never get any problems on any other hosting and the fact I host over 50 sites across servers you'd think their support team would kinda relate to their own security being the problem. Performance Wise on Shared Hosting, REALLY POOR and VPS well its a VPS with hardly any perks and weak support.
You should get a VPS that has more than 512mb ram or 384mb using a SWAP. The few I know of and you want max reliability and your pretty new to VPS and will require some support then go Rackspace, if you tight for cash and want to test VPS without paying then Amazon Micro instances are great. If you want max bang for Buck then CloudShards and if your a GoDaddy fan boy then /facepalm.
Hope this helps thanks.