You don't really need a sharpening stone, a strop will keep your razor in good order for a long time but you should have them professionally honed 1st. Even if you do buy a hone having them sharpened by someone who knows what they are doing will
- Show you what sharp really means, so you know what to aim for when you start to hone.
- Remove one of the variables from learning how to use a straight.
Learning how to shave with a straight is a reasonably steep learning curve so eliminating the question of whether the razor is sharp enough really helps.
If once you have a grasp of shaving, if think you want to maintain your razors yourself you have a choice of using a strop with an abrasive paste or powder, a barbers hone or a finishing stone to touch up the edge and keep it going (I have listed them roughly in the order of cost).
Pasted strops: There are various compounds to bring an edge back to near peak, such as chromium oxide, diamond spray and plenty more. As I understand it they do over time weaken the edge which is why many people go for hones but they will keep the edge good for much longer than stropping alone.
Barbers hones: These come up on Ebay quite regularly and are useful but I don't think they give as refined an edge as a finishing stone. I.e. they are perfectly satisfactory but I prefer an edge which is approaching awesome. I got mine for about £5 but I have also seen them make £25+.
Finishing stones: These come in various forms, the cheapest is the so called Chinese 12K waterstone available on ebay and from the invisible edge for less than £20. There is a widespread belief that they are not really as fine as 12k but none the less they are excellent value for money but a very slow stone which take a quite a bit of work to get the best from. There are some dear vintage finishers such as charnley forests and eschers which will set you back well over £100 unless you are lucky so again unless you get into restoring and selling razors its probably not worth the money. Coticules and a Naniwa 12k super stone come in around the £60 mark and will give a great edge albeit coticules are a natural stone and some are better finishers than others they are available from Eden Webshop and The Invisible Edge.
Neil Miller also keeps a wide range of stones but they tend to be those lovely vintage gems and as such carry an appropriate price tag.
You would not typically need a full range of stones, unless you want to take a razor which hasn't been used for many years from totally dull to shave ready and even then if its only a couple you want sorting then its cheaper to have them honed than buy the stones to do it yourself.