As harpune1 said, 90/100cm is probably a good starting point. The
sumora, official distributors of Rabitech and Rob Allen website in the USA has a
useful table that provides advice on the length of speargun to get -- which depends on the visibility of the water you dive and the terrain (reef/open water/kelp/lake/...). Here is the UK the usual recommendation is 75-90cm, in the med. 100cm seems more common (& perhaps a shorter cave gun?). South Africa, 110cm-150cm are not uncommon.
If you fill in the location field of your profile, somebody in your area might be able to provide a better guide for you. If you'll be shooting mainly big fish, you might want more or heavier elastic bands and a thicker than normal spear.
It is hard to recommend a "good gun for a beginner" because if you take to spearing you'll wish you'd got a good one & if you rarely use it you'll wish you didn't

. They all work. I would suggest getting a mid-priced well known brand on band gun (so you can sell it easily & get parts & service if necessary) - e.g. Omer, Cressi, Rob Allen, Seatec (don't know much about the wooden US guns - JBL, A.B. Biller, Wong & Riffe). They do cut corners on some of the very cheapest spearguns, so check details if going for a real low-end gun, but you can always upgrade rubbers & wishbone and add a muzzle bungee later if you feel the need. Omer is a spearo specialist company with a wide range of products that seem to offer excellent service by a forum member Mark Laboccetta in the USA; if I were still in the USA I would probably try there first. (In Europe, try
Spearguns by Spearo uk ltd finest supplier of speargun, monofins, speargun and freediving equipment - always an interesting selection, good beginner articles too, or apnea.co.uk or Portland Oceaneering).