If you are looking to spend £100-150 then you could be alright for a decent Henry VIII halfgroat or sovereign penny. You will struggle if you are looking for the Holbein portrait on a coin however, as a testoon with a decent portrait is measured in thousands. To give you an idea of the grade you could expect to find, a few images are attached for the Tudors.
First up is a 2nd coinage 2d struck at York under Abp. Lee - about 18mm dia..
Second is a sovereign penny. There are several types of this and not all are equal. The portrait on this one is a bit better than you might expect for the money you want to spend, but a clear portrait of the king seated on the throne should be possible. About 15mm dia.
Third coin. Henry VII you can get a middle grade groat (4d) of the commoner types or mintmark - about 25mm dia. You could also get a halfgroat (2d) of this reign in reasonable condition.
Halfpennies of Henry VII, Henry VIII and Elizabeth I will be at the bottom end of the price range for a decent example, but are quite small at 11 or 12mm dia. Fourth, the Henrys are a facing bust. 5th, the Elizabeth design is a portcullis.
You are unlikely to find much in the way of Edward VI or Mary in your price range, but might be able to find a lower grade fine silver issue shilling of the former.
A shilling is possible for Elizabeth 1 as is a sixpence, threepence or smaller, but a rule of thumb is the larger the coin, the more expensive they tend to be for the generic types. Portraits on Eliz.1 shillings tend to be quite weak, so this might not be the best option if you want a coin in better condition. A sixpence with a decent portrait would be better (6th coin) as these come better struck up.
This isn't exhaustive, but gives a few options.