You have several options, but remmenber that orchard 1.6 needs to run on full trust.
I use this company on some sites i built for my customers and works very well, they even have 24h support:
Bertrand Leroy also has mentioned in these foruns that this company works well, and he is hosting is ecommerce nwazet.com site there:
You can also go for Azure Websites they even give you a 3 Month trial.
These are just a few, but surely that there are lot more that will satisfy your needs.
As an advice i would like to tell you that I get pretty good performance with shared hosting on low traffic websites by using WarmUp and KeepAlive modules.